]>
2016
9
5
ISSN 2008-1898
1506
Remark on fundamentally non-expansive mappings in hyperbolic spaces
Remark on fundamentally non-expansive mappings in hyperbolic spaces
en
en
In this paper, we prove some properties of fixed point set of fundamentally non-expansive mappings
and derive the existence of fixed point theorems as follows results of Salahifard et al. [H. Salahifard, S. M.
Vaezpour, S. Dhompongsa, J. Nonlinear Anal. Optim., 4 (2013), 241-248] in hyperbolic spaces.
1952
1956
Cholatis
Suanoom
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
Cholatis.Suanoom@gmail.com
Chakkrid
Klin-eam
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
chakkridk@nu.ac.th
Fixed point set
fundamentally non-expansive mappings
\(\triangle\)-closed set
convex set
hyperbolic spaces.
Article.1.pdf
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[1]
S. Chang, G. Wang, L. Wang, Y. K. Tang, Z. L. Zhao, \(\triangle\)-convergence theorems for multi-valued nonexpansive mappings in hyperbolic spaces, Appl. Math. Comput., 249 (2014), 535-540
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S. J. H. Ghoncheh, A. Razani, Fixed point theorems for some generalized nonexpansive mappings in Ptolemy spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
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L. Leustean, A quadratic rate of asymptotic regularity for CAT(0)-spaces, J. Math. Anal. Appl., 325 (2007), 386-399
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L. Leustean, Nonexpansive iterations in uniformly convex W-hyperbolic spaces , Nonlinear Anal. Optim., 513 (2010), 193-209
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T. C. Lim, Remarks on some fixed point theorems, Proc. Am. Math. Soc., 60 (1976), 179-182
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H. Salahifard, S. M. Vaezpour, S. Dhompongsa, Fixed point theorems for some generalized nonexpansive mappings in CAT(0) spaces, J. Nonlinear Anal. Optim., 4 (2013), 241-248
##[8]
T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings , J. Math. Anal. Appl., 340 (2008), 1088-1095
]
Fixed point theorem and nonlinear complementarity problem in Hilbert spaces
Fixed point theorem and nonlinear complementarity problem in Hilbert spaces
en
en
In this paper, the concept of the strongly monotone type mapping is introduced, which contains the
strongly monotone mapping and firmly type nonexpansive mapping as special cases. We show the equivalence
between the fixed point problem and the complementarity problem of strongly monotone type mapping.
Furthermore, it is obtained that an iteration sequence strongly converges to a unique solution of such a
nonlinear complementarity problem on the proper conditions. The error estimation of such an iteration is
discussed.
1957
1964
Hongjun
Wang
School of Mathematics and Information Science and Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control
Henan Normal University
P. R. China
hsdwhj@163.com
Yuchun
Zheng
School of Mathematics and Information Science and Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control
Henan Normal University
P. R. China
zhengyuchun1@yeah.net
Fixed point
strongly monotone type
complementarity problem
iteration.
Article.2.pdf
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]
A Lyapunov-type inequality for a fractional q-difference boundary value problem
A Lyapunov-type inequality for a fractional q-difference boundary value problem
en
en
In this paper, we establish a Lyapunov-type inequality for a fractional q-difference equation subject to
Dirichlet-type boundary conditions. The obtained inequality generalizes several existing results from the
literature including the standard Lyapunov inequality. We use that result to provide an interval, where
a certain Mittag-Leffler function has no real zeros. We present also another application of the obtained
inequality, where we prove that existence implies uniqueness for a certain class of fractional q-difference
boundary value problems.
1965
1976
Mohamed
Jleli
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
jleli@ksu.edu.sa
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
Lyapunov's inequality
q-fractional derivative
Green's function
Mittag-Leffler function.
Article.3.pdf
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M. F. Aktas, Lyapunov-type inequalities for a certain class of n-dimensional quasilinear systems, Electron. J. Differ. Equat., 67 (2013), 1-8
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D. Çakmak, Lyapunov-type integral inequalities for certain higher order differential equations, Appl. Math. Comput., 216 (2010), 368-373
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D. Ç akmak, On Lyapunov-type inequality for a class of nonlinear systems, Math. Inequal. Appl., 16 (2013), 101-108
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M. El-Shahed, H. A. Hassan, Positive solutions of q-difference equation, Proc. Amer. Math. Soc., 138 (2010), 1733-1738
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R. A. C. Ferreira, Nontrivial solutions for fractional q-difference boundary value problems, Electron. J. Qual. Theory Differ. Equ., 70 (2010), 1-10
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R. A. C. Ferreira, Positive solutions for a class of boundary value problems with fractional q-differences , Comput. Math. Appl., 61 (2011), 367-373
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier, Amsterdam (2006)
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]
Fixed point theorems for (\(\alpha,\eta,\psi,\xi\))-contractive multi-valued mappings on \(\alpha-\eta\)-complete partial metric spaces
Fixed point theorems for (\(\alpha,\eta,\psi,\xi\))-contractive multi-valued mappings on \(\alpha-\eta\)-complete partial metric spaces
en
en
In this paper, the notion of strictly (\(\alpha,\eta,\psi,\xi\))-contractive multi-valued mappings is introduced where
the continuity of \(\xi\) is relaxed. The existence of fixed point theorems for such mappings in the setting of
\(\alpha,\eta\)-complete partial metric spaces are provided. The results of the paper can be viewed as the extension
of the recent results obtained in the literature. Furthermore, we assure the fixed point theorems in partial
complete metric spaces endowed with an arbitrary binary relation and with a graph using our obtained
results.
1977
1990
Ali
Farajzadeh
Department of Mathematics, Faculty of Science
Razi University
Iran
farajzadehali@gmail.com
Preeyaluk
Chuadchawna
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
Chuadchawna@hotmail.com
Anchalee
Kaewcharoen
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
anchaleeka@nu.ac.th
\(\alpha،\eta\)-complete partial metric spaces
\(\alpha،\eta\)-continuity
(\(\alpha،\eta،\psi،\xi\))-contractive multi-valued mappings
\(\alpha\)-admissible multi-valued mappings with respect to \(\eta\).
Article.4.pdf
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M. U. Ali, T. Kamran, E. Karapinar , (\(\alpha,\psi,\xi\))-Contractive multi-valued mappings, Fixed point theory Appl., 2014 (2014), 1-8
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I. Altun, H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud., 1 (2008), 1-8
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I. Altun, F. Sola, H. Simsek, Generalized contraction on partial metric spaces, Topology Appl., 157 (2010), 2778-2785
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P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized \(\alpha-\psi\)-contractions, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math., 108 (2014), 519-526
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H. Aydi , Some fixed point results in ordered partial metric spaces, J. Nonlinear Sci. Appl., 4 (2011), 210-217
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H. Aydi, Common fixed point for four maps in ordered partial metric spaces, Fasc. Math., 49 (2012), 15-31
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H. Aydi, M. Abbas, C. Vetro , Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces , Topology Appl., 159 (2012), 3234-3242
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N. Hussain, M. A. Kutbi, P. Salimi , Fixed point theory in \(\alpha\)-complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 1-11
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M. A. Kutbi, W. Sintunavrat, On new fixed pont results for (\(\alpha,\psi,\xi\))-contractive multi-valued mappings on \(\alpha\)- complete metric spaces and their consequences, Fixed point theory Appl., 2015 (2015), 1-15
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B. Mohammadi, S. Rezapour, S. Naseer , Some results on fixed points of \(\alpha-\psi\)-Ciric generalized multifunction, Fixed point theory Appl., 2013 (2013), 1-10
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]
Fixed-point theorem for Caputo--Fabrizio fractional Nagumo equation with nonlinear diffusion and convection
Fixed-point theorem for Caputo--Fabrizio fractional Nagumo equation with nonlinear diffusion and convection
en
en
We make use of fractional derivative, recently proposed by Caputo and Fabrizio, to modify the nonlinear Nagumo diffusion and convection equation. The proposed fractional derivative has no singular kernel
considered as a filter. We examine the existence of the exact solution of the modified equation using the
method of fixed-point theorem. We prove the uniqueness of the exact solution and present some numerical
simulations.
1991
1999
Rubayyi T.
Alqahtani
Department of Mathematics and Statistics, College of Science
Al-Imam Mohammad Ibn Saud Islamic University (IMSIU)
Saudi Arabia
rtalqahtani@imamu.edu.sa
Nonlinear Nagumo equation
Caputo-Fabrizio derivative
fixed-point theorem
uniqueness.
Article.5.pdf
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A. Atangana, On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation, Appl. Math. Comput., 273 (2016), 948-956
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A. Atangana, B. S. T. Alkahtani , Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel , Adv. Mech. Eng., 7 (2015), 1-6
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A. Atangana, S. C. Oukouomi Noutchie, On the fractional Nagumo equation with nonlinear diffusion and convection, Abstr Appl. Anal., 2014 (2014), 1-7
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M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel , Progr. Fract. Differ. Appl., 1 (2015), 73-85
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]
Cyclic hybrid methods for finding common fixed points of a finite family of nonexpansive mappings
Cyclic hybrid methods for finding common fixed points of a finite family of nonexpansive mappings
en
en
In this paper, we propose a cyclic hybrid method for computing a common fixed point of a finite family
of nonexpansive mappings. The strong convergence of the method is established. Numerical examples
illustrate that the proposed method has an advantage in computing.
2000
2005
Qiao-Li
Dong
College of Science
Tianjin Key Lab for Advanced Signal Processing
Civil Aviation University of China
Civil Aviation University of China
China
China
Yan-Yan
Lu
College of Science
Civil Aviation University of China
China
Jinfeng
Yang
Tianjin Key Lab for Advanced Signal Processing
Civil Aviation University of China
China
jfyang@cauc.edu.cn
Common fixed point
hybrid method
cyclic computation
nonexpansive mapping.
Article.6.pdf
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[1]
P. K. Anh, C. V. Chung , Parallel hybrid methods for a finite family of relatively nonexpansive mappings, Numer. Func. Anal. Optim., 35 (2014), 649-664
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H. H. Bauschke, P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, Berlin (2011)
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L. C. Ceng, N. C. Wong, J. C. Yao , Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications, Fixed Point Theory Appl., 2012 (2012), 1-21
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Y. Censor, T. Elfving , A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
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Y. Censor, T. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems , Inverse Problems, 21 (2005), 2071-2084
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J. P. Chancelier , Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces , J. Math. Anal. Appl., 353 (2009), 141-153
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Q. L. Dong, Y. Y. Lu , A new hybrid algorithm for a nonexpansive mapping, Fixed Point Theory Appl., 2015 (2015), 1-7
##[8]
Q. L. Dong, H. B. Yuan, Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping , Fixed Point Theory Appl., 2015 (2015), 1-12
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S. He, C. Yang, P. Duan , Realization of the hybrid method for Mann iterations , Appl. Math. Comput., 217 (2010), 4239-4247
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K. Goebel, W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
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C. Martinez-Yanes, H. K. Xu , Strong convergence of the CQ method for fixed point iteration processes , Nonlinear Anal., 64 (2006), 2400-2411
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K. Nammanee, R. Wangkeeree, New iterative approximation methods for a countable family of nonexpansive mappings in Banach spaces, Fixed Point Theory Appl., 2011 (2011), 1-24
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W. Nilsrakoo, S. Saejung, Weak and strong convergence theorems for countable Lipschitzian mappings and its applications, Nonlinear Anal., 69 (2008), 2695-2708
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W. Takahashi, Y. Takeuchi, R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 341 (2008), 276-286
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L. Wei, Y. J. Cho, H. Y. Zhou, A strong convergence theorem for common fixed points of two relatively nonexpansive mappings and its applications, J. Appl. Math. Comput., 29 (2009), 95-103
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Y. Yao, Y. C. Liou, N. C. Wong, Iterative algorithms based on the implicit midpoint rule for nonexpansive mappings, J. Nonlinear Convex A., (preprint), -
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Y. Yao, M. Postolache, Y. C. Liou, Z. Yaz , Construction algorithms for a class of monotone variational inequalities, Optim. Lett., (in press), -
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H. Zhou, Y. Su , Strong convergence theorems for a family of quasi-asymptotic pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 4047-4052
]
Shadowing orbits of stochastic differential equations
Shadowing orbits of stochastic differential equations
en
en
This paper is devoted to the existence of a true solution near a numerical approximate solution of stochastic
differential equations. We prove a general shadowing theorem for finite time of stochastic differential
equations under some suitable conditions and provide an estimate of shadowing distance by computable
quantities. The practical use of this theorem is demonstrated in the numerical simulations of chaotic orbits
of the stochastic Lorenz system.
2006
2018
Qingyi
Zhan
College of Computer and Information Science
Fujian Agriculture and Forestry University
P. R. China
zhanqy@lsec.cc.ac.cn
Stochastic differential equations
random dynamical system
shadowing
multiplicative ergodic theorem
stochastic Lorenz system.
Article.7.pdf
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L. Arnold, Random Dynamical Systems, Springer-Verlag, Berlin (2003)
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L. Arnold, B. Schmalfuss , Lyapunov's second method for random dynamical systems, J. Differential Equations, 177 (2001), 235-265
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J. Duan , An introduction to stochastic dynamics, Cambridge University Press, New York (2015)
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A. Fakhari, A. Golmakani , Shadowing properties of random hyperbolic sets , Internat. J. Math., 23 (2012), 1-10
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G. H. Golub, C. F. Van Loan , Matrix computations , Johns Hopkins University Press, Baltimore (2013)
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J. Hong, R. Scherer, L. Wang, Midpoint rule for a linear stochastic oscillator with additive noise , Neural Parallel Sci. Comput., 14 (2006), 1-12
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H. Keller , Attractors and bifurcations of stochastic Lorenz system, in ''Technical Report 389'',Institut fur Dynamische Systeme, Universitat Bremen (1996)
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K. J. Palmer, Shadowing in dynamical systems, Theory and applications, Kluwer Academic Publishers, Dordrecht (2000)
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X. Xie, Q. Zhan , Uniqueness of limit cycles for a class of cubic system with an invariant straight line , Nonlinear Anal., 70 (2009), 4217-4225
]
Stabilization of a nonlinear control system on the Lie group \( SO(3)\times \mathbb{R}^3\times \mathbb{R}^3 \)
Stabilization of a nonlinear control system on the Lie group \( SO(3)\times \mathbb{R}^3\times \mathbb{R}^3 \)
en
en
The stabilization of some equilibrium points of a dynamical system via linear controls is studied. Numerical integration using Lie-Trotter integrator and its properties are also presented.
2019
2030
Camelia
Petrişor
Department of Mathematics
Politehnica University of Timişoara
România
camelia.petrisor@upt.ro
Optimal control problem
Hamilton-Poisson system
nonlinear stability
numerical integration.
Article.8.pdf
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]
Sharp bounds for Neuman means with applications
Sharp bounds for Neuman means with applications
en
en
In the article, we present the sharp bounds for the Neuman mean NAG(a; b), \(N_{GA}(a; b), N_{QA}(a; b)\)
and \(N_{AQ}(a; b)\) in terms of the convex combinations of the arithmetic and one-parameter harmonic and
contraharmonic means. As applications, we find several sharp inequalities for the first Seiffert, second
Seiffert, Neuman-Sándor and logarithmic means.
2031
2038
Fang-Li
Xia
School of Mathematics and Computation Sciences
Hunan City University
China
xiafangli2005@126.com
Wei-Mao
Qian
School of Distance Education
Huzhou Broadcast and TV University
China
qwm661977@126.com
Shu-Bo
Chen
School of Mathematics and Computation Sciences
Hunan City University
China
shubo.chen@163.com
Yu-Ming
Chu
School of Mathematics and Computation Sciences
Hunan City University
China
chuyuming2005@126.com
Neuman mean
Schwab-Borchardt mean
harmonic mean
geometric mean
arithmetic mean
quadratic mean
contra-harmonic mean.
Article.9.pdf
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]
Demagnetization fault detection in permanent magnet synchronous motors based on sliding observer
Demagnetization fault detection in permanent magnet synchronous motors based on sliding observer
en
en
This paper considers a robust multiple fault detection method for actuator failures in nonlinear systems.
The actuator failures model is initially put forward. By employing the unique advantage that the sliding
mode variable structure is invariance to uncertainties, a sliding mode state observer is designed to isolate the
unknown input disturbance effect on residual generation. The parameters of the observers being designed are
determined by the use of linear matrix inequalities techniques. Accordingly, the generated residual is only
sensitive to the specific fault signals, and the fault detection accuracy is improved. This paper verifies the
proposed method by its application in demagnetization fault detection for a permanent magnet synchronous
motor (PMSM). Simulation and experiment results illustrate the high detection accuracy and robustness.
2039
2048
Jing
He
School of Electrical and Information Engineering
School of Mechatronic Engineering and Automation
Hunan University of Technology
National University of Defense Technology
China
China
hejing@263.net
Changfan
Zhang
School of Electrical and Information Engineering
Hunan University of Technology
China
zhangchangfan@263.net
Songan
Mao
School of Electrical and Computer Engineering
Purdue University
U. S. A.
songan@purdue.edu
Han
Wu
School of Electrical and Information Engineering
Hunan University of Technology
China
wuhan90@163.com
Kaihui
Zhao
School of Electrical and Information Engineering
Hunan University of Technology
China
zhaokaihui@outlook.com
Fault detection
sliding mode variable structure
state observer
residual
permanent magnet synchronous motor.
Article.10.pdf
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K. Y. Lian, C. H. Chiang, H. W. Tu, LMI-based sensorless control of permanent-magnet synchronous motors, IEEE T. Ind. Electron., 54 (2007), 2769-2778
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X. Xiao, M. Zhang, Y. D. Li , On-line estimation of permanent-magnet flux linkage ripple for PMSM, Proc. CSEE, 27 (2007), 43-47
]
Unified implicit common fixed point theorems under non-negative complex valued functions satisfying the identity of indiscernible
Unified implicit common fixed point theorems under non-negative complex valued functions satisfying the identity of indiscernible
en
en
In this paper, we consider a non-negative complex valued function satisfying the identity of indiscernible
and utilize the same to prove some common fixed point theorems for two pairs of non-vacuously weakly compatible mappings satisfying an implicit relation having rational terms as its co-ordinates. Some illustrative
examples are also given which demonstrate the validity of the hypotheses of our results. In process, a host
of previously known results in the context of complex as well as real valued metric spaces are generalized
and improved.
2049
2069
Deepak
Singh
Department of Applied Sciences
NITTTR, Under Ministry of HRD, Govt. of India
India
dk.singh1002@gmail.com
Vishal
Joshi
Department of Applied Mathematics
Jabalpur Engineering College
India
joshinvishal76@gmail.com
Mohammad
Imdad
Department of Mathematics
Aligarh Muslim University
India
mhimdad@gmail.com
Poom
Kumam
Department of Mathematics & Theoretical and Computational Science (TaCS) Center, Faculty of Science
King Mongkut's University of Technology Thonburi (KMUTT)
China Medical University
Thailand
Taiwan
poom.kum@kmutt.ac.th;poom.kum@mail.cmu.edu.tw
Complex valued metric spaces
non-vacuously weakly compatible mappings
implicit relations
coincidence point
point of coincidence
fixed point.
Article.11.pdf
[
[1]
J. Ahmed, A. Azam, S. Saejung, Common fixed point results for contractive mappings in complex valued metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
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A. Ali, M. Imdad , An implicit function implies several contraction conditions, Sarajevo J. Math., 4 (2008), 269-285
##[3]
A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Func. Anal. Optim., 32 (2011), 243-253
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A. Bhatt, H. Chandra, D. R. Sahu , Common fixed point theorems for occasionally weakly Compatible mappings under relaxed conditions, Nonlinear Anal., 73 (2010), 176-182
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S. Bhatt, S. Chaukiyal, R. C. Dimri, A common fixed point theorem for weakly compatible maps in complex valued metric spaces, Int. J. Math. Sci. Appl., 1 (2011), 1385-1389
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S. K. Datta, S. Ali, A common fixed point theorem under contractive condition in complex valued metric spaces, Int. J. Adv. Sci. Tech. Research, 6 (2012), 467-475
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D. Gopal, M. Imdad, Some new common fixed point theorems in fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat., 57 (2011), 303-316
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M. Imdad, J. Ali , A general fixed point theorem in fuzzy metric spaces via an implicit function, J. Appl. Math. Info., 26 (2008), 591-603
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G. Jungck, B. E. Rhoades , Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, 7 (2006), 286-296
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H. K. Nashine, M. Imdad, H. Hasan, Common fixed point theorems under rational contractions in complex valued metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 42-50
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K. P. R. Rao, P. Rangaswamy, J. R. Prasad, A common fixed point theorem in complex valued b-metric spaces, Bull. Math. Stat. Res., 1 (2013), 1-8
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F. Rouzkard, M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl., 64 (2012), 1866-1874
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K. P. R. Sastry, G. A. Naidu, T. Bekeshie, M. A. Rahamatulla, A common fixed point theorem for four self maps in complex valued and vector valued metric spaces, Int. J. Math. Arc., 3 (2012), 2680-2685
##[20]
R. K. Verma, H. K. Pathak, Common fixed point theorems using property (E.A) in complex-valued metric spaces, Thai J. Math., 11 (2013), 347-355
]
Hyers--Ulam stability of nth order linear differential equations
Hyers--Ulam stability of nth order linear differential equations
en
en
For nth order linear homogeneous and nonhomogeneous differential equations with nonconstant coefficients, we prove Hyers{Ulam stability by using open mapping theorem. The generalized Hyers{Ulam
stability is also investigated.
2070
2075
Tongxing
Li
School of Informatics
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
Linyi University
Linyi University
P. R. China
P. R. China
litongx2007@163.com
Akbar
Zada
Department of Mathematics
University of Peshawar
Pakistan
zadababo@yahoo.com
Shah
Faisal
Department of Mathematics
University of Peshawar
Pakistan
shahfaisal8763@gmail.com
Hyers-Ulam stability
generalized Hyers-Ulam stability
nth order linear differential equation
open mapping theorem.
Article.12.pdf
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M. Burger, N. Ozawa, A. Thom , On Ulam stability, Israel J. Math., 193 (2013), 109-129
##[6]
G. Choi, S.-M. Jung, Invariance of Hyers-Ulam stability of linear differential equations and its applications, Adv. Difference Equ., 2015 (2015), 1-14
##[7]
J. Chung, Hyers-Ulam stability theorems for Pexider equations in the space of Schwartz distributions , Arch. Math., 84 (2005), 527-537
##[8]
J. Huang, S.-M. Jung, Y. Li , On Hyers-Ulam stability of nonlinear differential equations , Bull. Korean Math. Soc., 52 (2015), 685-697
##[9]
J. Huang, Y. Li, Hyers-Ulam stability of linear functional differential equations, J. Math. Anal. Appl., 426 (2015), 1192-1200
##[10]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224
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S.-M. Jung , Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett., 17 (2004), 1135-1140
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S.-M. Jung , Hyers-Ulam stability of linear differential equations of first order, III, J. Math. Anal. Appl., 311 (2005), 139-146
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S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order, II, Appl. Math. Lett., 19 (2006), 854-858
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Y. Li, Y. Shen , Hyers-Ulam stability of linear differential equations of second order, Appl. Math. Lett., 23 (2010), 306-309
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G. Wang, M. Zhou, L. Sun, Hyers-Ulam stability of linear differential equations of first order , Appl. Math. Lett., 21 (2008), 1024-1028
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A. Zada, O. Shah, R. Shah, Hyers-Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems, Appl. Math. Comput., 271 (2015), 512-518
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]
Existence of positive solution for a fractional order nonlinear differential system involving a changing sign perturbation
Existence of positive solution for a fractional order nonlinear differential system involving a changing sign perturbation
en
en
In this paper, we study a class of singular fractional order differential system with a changing-sign
perturbation which arises from
uid dynamics, biological models, electrical networks with uncertain physical
parameters and parametrical variations in time. Under suitable growth condition, the singular changing-
sign system is transformed to an approximately singular fractional order differential system with positive
nonlinear term, then the existence of positive solution is established by using the known fixed point theorem.
2076
2085
Jianxin
He
School of Science
School of Science
Nanjing University of Science and Technology
Nanjing University of Posts and Telecommunications
P. R. China
P. R. China
hjx_cheng@163.com
Xinguang
Zhang
School of Mathematical and Informational Sciences
Department of Mathematics and Statistics
Yantai University
Curtin University of Technology
China
Australia
zxg123242@163.com
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University of Technology
Australia
y.wu@curtin.edu.au
Singular phenomena
changing-sign perturbation
positive solution
Riemann-Stieltjes integral conditions.
Article.13.pdf
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R. Agarwal, D. O'Regan, A note on existence of nonnegative solutions to singular semi-positone problems, Non-linear Anal., 36 (1999), 615-622
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Z. Bai, H. Lv, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311 (2005), 495-505
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Y. Q. Chen, H. S. Ahn, I. Podlubny , Robust stability check of fractional order linear time invariant systems with interval uncertainties, Proc. IEEE Int. Conference Mech. Automation, 1 (2005), 210-215
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D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cone, Academic Press, Inc., New York (1988)
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S. Hosseinnia, R. Ghaderi, A. Ranjbar, M. Mahmoudian, S. Momani , Sliding mode synchronization of an uncertain fractional order chaotic system, Comput. Math. Appl., 59 (2010), 1637-1643
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A. Kilbas, H. Srivastava, J. Trujillo , Theory and Applications of Fractional Differential Equations, Elsevier B.V, Netherlands (2006)
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Y. H. Lan, Y. Zhou, LMI-based robust control of fractional-order uncertain linear systems, Comput. Math. Appl., 62 (2011), 1460-1471
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S. Li, X. Zhang, Y. Wu, L. Caccetta, Extremal solutions for p-Laplacian differential systems via iterative computation, Appl. Math. Lett., 26 (2013), 1151-1158
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Z. Liao, C. Peng, W. Li, Y. Wang, Robust stability analysis for a class of fractional order systems with uncertain parameters, J. Franklin Inst., 348 (2011), 1101-1113
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T. Lin, T. Lee , Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control, IEEE Trans. Fuzzy Sys., 19 (2011), 623-635
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R. Ma, R. Wang, L. Ren, Existence results for semipositone boundary value problems, Acta Math. Sci. Ser. B Engl. Ed., 21 (2001), 189-195
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I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York (1999)
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X. Zhang, Y. Han, Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations, Appl. Math. Lett., 25 (2012), 555-560
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X. Zhang, L. Liu , Positive solutions of superlinear semipositone singular Dirichlet boundary value problems , J. Math. Anal. Appl., 316 (2006), 525-537
##[16]
X. Zhang, L. Liu, Multiple positive solutions of a singular fractional differential equation with negatively perturbed term, Math. Compu. Modelling, 55 (2012), 1263-1274
##[17]
X. Zhang, L. Liu, B. Wiwatanapataphee, Y. Wu , The eigenvalue for a class of singular p-Laplacian fractional differential equations involving the Riemann-Stieltjes integral boundary condition, Appl. Math. Comput., 235 (2014), 412-422
##[18]
X. Zhang, L. Liu, Y. Wu , Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives, Appl. Math. Comput., 219 (2012), 1420-1433
##[19]
X. Zhang, L. Liu, Y. Wu, The eigenvalue problem for a singular higher fractional differential equation involving fractional derivatives, Appl. Math. Comput., 218 (2012), 8526-8536
##[20]
X. Zhang, L. Liu, Y. Wu, The uniqueness of positive solution for a singular fractional differential system involving derivatives, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 1400-1409
##[21]
X. Zhang, L. Liu, Y. Wu , The uniqueness of positive solution for a fractional order model of turbulent flow in a porous medium , Appl. Math. Lett., 37 (2014), 26-33
##[22]
X. Zhang, L. Liu, Y. Wu , Variational structure and multiple solutions for a fractional advection-dispersion equation, Comput. Math. Appl., 68 (2014), 1794-1805
##[23]
X. Zhang, L. Liu, Y. Wu, Y. Lu , The iterative solutions of nonlinear fractional differential equations, Appl. Math. Comput., 219 (2013), 4680-4691
##[24]
X. Zhang, Y. Wu, L. Caccetta, Nonlocal fractional order differential equations with changing-sign singular perturbation, Appl. Math. Model., 39 (2015), 6543-6552
]
Identities involving degenerate Euler numbers and polynomials arising from non-linear differential equations
Identities involving degenerate Euler numbers and polynomials arising from non-linear differential equations
en
en
The purpose of this paper is to construct some new non-linear differential equations and investigate
the solutions of these non-linear differential equations. In addition, we give some new identities involving
degenerate Euler numbers and polynomials arising from those non-linear differential equations.
2086
2098
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Degenerate Euler numbers
degenerate Euler polynomials
non-linear differential equation
degenerate Bernoulli numbers
degenerate Bernoulli polynomials
Article.14.pdf
[
[1]
A. Bayad, T. Kim, Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials, Russ. J. Math. Phys., 18 (2011), 133-143
##[2]
L. Carlitz , A degenerate Staudt-Clausen theorem, Arch. Math. (Basel), 7 (1956), 28-33
##[3]
L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51-88
##[4]
D. Ding, J. Yang , Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 20 (2010), 7-21
##[5]
S. Gaboury, R. Tremblay, B. J. Fugère, Some explicit formulas for certain new classes of Bernoulli, Euler and Genocchi polynomials, Proc. Jangjeon Math. Soc., 17 (2014), 115-123
##[6]
L.-C. Jang, B. M. Kim , On identities between sums of Euler numbers and Genocchi numbers of higher order, J. Comput. anal. appl., 20 (2016), 1240-1247
##[7]
D. Kang, J. Jeong, S.-J. Lee, S.-H. Rim, A note on the Bernoulli polynomials arising from a non-linear differential equation, Proc. Jangjeon Math. Soc., 16 (2013), 37-43
##[8]
T. Kim , Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., 16 (2009), 93-96
##[9]
T. Kim , Corrigendum to ''Identities involving Frobenius-Euler polynomials arising from non-linear differential equations'' [J. Number Theory, 132 (12) (2012), 2854-2865], J. Number Theory, 133 (2013), 822-824
##[10]
T. Kim, Degenerate Euler zeta function, Russ. J. Math. Phys., 22 (2015), 469-472
##[11]
D. S. Kim, T. Kim, Some identities for Bernoulli numbers of the second kind arising from a non-linear differential equation, Bull. Korean Math. Soc., 52 (2015), 2001-2010
##[12]
D. S. Kim, T. Kim, Some identities of degenerate Euler polynomials arising from p-adic fermionic integrals on \(\mathbb{Z}_p\), Integral Transforms Spec. Funct., 26 (2015), 295-302
##[13]
G. Kim, B. Kim, J. Choi, The DC algorithm for computing sums of powers of consecutive integers and Bernoulli numbers , Adv. Stud. Contemp. Math. (Kyungshang), 17 (2008), 137-145
##[14]
C. S. Ryoo, Some relations between twisted q-Euler numbers and Bernstein polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 21 (2011), 217-223
##[15]
E. Şen, Theorems on Apostol-Euler polynomials of higher order arising from Euler basis, Adv. Stud. Contemp. Math. (Kyungshang), 23 (2013), 337-345
]
On Opial-Rozanova type inequalities
On Opial-Rozanova type inequalities
en
en
In the present paper we establish some inverses of Rozanova's type integral inequalities. The results in
special cases yield reverse Rozanova's, Godunova's and Pölya's inequalities.
2099
2104
Chang-Jian
Zhao
Department of Mathematics
China Jiliang University
China
chjzhao@163.com;chjzhao@aliyun.com
Yue-Sheng
Wu
Department of Mathematics
China Jiliang University
China
wuys@cjlu.edu.cn
Wing-Sum
Cheung
Department of Mathematics
The University of Hong Kong
Hong Kong
wscheung@hku.hk
Opial's inequality
Jensen's inequality
Rozanova's inequality.
Article.15.pdf
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C. J. Zhao, W. S. Cheung, Reverse Hilbert's type integral inequalities , Math. Ineq. Appl., 17 (2014), 1551-1561
]
Existence results for three-point boundary value problems for nonlinear fractional differential equations
Existence results for three-point boundary value problems for nonlinear fractional differential equations
en
en
In this paper, we study a new class of nonlinear fractional differential equations with three-point boundary
conditions. Existence of solutions are obtained by using Krasnoselskii's fixed point theorem and Leray-Schauder nonlinear alternative. An illustrative example is presented at the end of the paper to illustrate
the validity of our results.
2105
2116
Sina
Etemad
Young Researchers and Elite Club
Tabriz Branch, Islamic Azad University
Iran
sina.etemad@gmail.com
Sotiris K.
Ntouyas
Department of Mathematics
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
University of Ioannina
King Abdulaziz University
Greece
Saudi Arabia
sntouyas@uoi.gr
Jessada
Tariboon
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
Centre of Excellence in Mathematics
King Mongkut's University of Technology North Bangkok
CHE
Thailand
Thailand
jessada.t@sci.kmutnb.ac.th
Fractional differential equation
boundary value problem
existence
fixed point theorem
three-point.
Article.16.pdf
[
[1]
R. P. Agarwal, D. Baleanu, V. Hedayati, Sh. Rezapour, Two fractional derivative inclusion problems via integral boundary condition, Appl. Math. Comput., 257 (2015), 205-212
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##[3]
B. Ahmad, Nonlinear fractional differential equations with anti-periodic type fractional boundary conditions, Differ. Equ. Dyn. Syst., 21 (2013), 387-401
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B. Ahmad, S. K. Ntouyas, Existence of solutions for nonlinear fractional q-difference inclusions with nonlocal Robin (separated) conditions, Mediter. J. Math., 10 (2013), 1333-1351
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Z. Bai, W. Sun, Existence and multiplicity of positive solutions for singular fractional boundary value problems, Comput. Math. Appl., 63 (2012), 1369-1381
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D. Baleanu, H. Mohammadi, Sh. Rezapour , The existence of solutions for a nonlinear mixed problem of singular fractional differential equations, Adv. Difference Equ., 2013 (2013), 1-12
##[8]
D. Baleanu, Sh. Rezapour, S. Etemad, A. Alsaedi, On a time-fractional integro-dierential equation via three-point boundary value conditions, Math. Probl. Eng., 2015 (2015), 1-12
##[9]
D. Baleanu, Sh. Rezapour, H. Mohammadi, Some existence results on nonlinear fractional differential equations , Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 371 (2013), 1-7
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K. Diethelm, Analysis of fractional differential equations, Springer-Verlag, Berlin (2010)
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X. Fu , Existence results for fractional differential equations by three-point boundary conditions, Adv. Difference Equ., 2013 (2013), 1-15
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R. Ghorbanian, V. Hedayati, M. Postolache, Sh. Rezapour, On a fractional differential inclusion via a new integral boundary condition, J. Inequal. Appl., 2014 (2014), 1-20
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S. K. Ntouyas, S. Etemad , On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions, Appl. Math. Comput., 266 (2015), 235-243
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L. Zhang, B. Ahmad, G. Wang, R. P. Agarwal , Nonlinear fractional integro-differential equations on unbounded domains in a Banach space, J. Comput. Appl. Math., 249 (2013), 51-56
]
A new numerical method for heat equation subject to integral specifications
A new numerical method for heat equation subject to integral specifications
en
en
We develop a numerical technique for solving the one-dimensional heat equation that combine classical
and integral boundary conditions. The combined Laplace transform, high-precision quadrature schemes,
and Stehfest inversion algorithm are proposed for numerical solving of the problem. A Laplace transform
method is introduced for solving considered equation, definite integrals are approximated by high-precision
quadrature schemes. To invert the equation numerically back into the time domain, we apply the Stehfest
inversion algorithm. The accuracy and computational efficiency of the proposed method are verified by
numerical examples.
2117
2125
H. M.
Jaradat
Department of Mathematics
Department of Mathematics and Applied Sciences
Al al-Bayt University
Dhofar University
Jordan
Oman
husseinjaradat@yahoo.com
M. M. M.
Jaradat
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
mmjst4@qu.edu.qa
F.
Awawdeh
Department of Mathematics
Department of Mathematics and Applied Sciences
Hashemite University
Dhofar University
Jordan
Oman
fawawadeh@du.edu.om
Z.
Mustafa
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
zead@qu.edu.qa
O.
Alsayyed
Department of Mathematics
Hashemite University.
Jordan
o.alsayyed@yahoo.com
Heat equation
nonlocal boundary value problems
Laplace inversion
high-precision quadrature schemes
Stehfest inversion algorithm.
Article.17.pdf
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]
Strong convergence of a modified SP-iteration process for generalized asymptotically quasi- nonexpansive mappings in CAT(0) spaces
Strong convergence of a modified SP-iteration process for generalized asymptotically quasi- nonexpansive mappings in CAT(0) spaces
en
en
In this paper, we establish strong convergence theorems of the modified SP-iteration generalized asymptotically quasi-nonexpansive mapping in CAT(0) spaces which extend and improve the recent ones announced
by Phuengrattana and Suantai [W. Phuengrattana, S. Suantai, J. Comput. Appl. Math., 235 (2011), 3006-
3014], Sahin and Basarir [A. Sahin, M. Basarir, J. Inequal. Appl., 2013 (2013), 10 pages], Nanjaras and
Panyanak [B. Nanjaras, B. Panyanak, Fixed Point Theory Appl., 2010 (2010), 14 pages] and some others.
2126
2135
Duangkamon
Kitkuan
Department of Mathematics, Faculty of Science and Technology
Rambhai Barni Rajabhat University (RBRU)
Thailand
or_duangkamon@hotmail.com
Anantachai
Padcharoen
Department of Mathematics, Faculty of Science and Technology
Rambhai Barni Rajabhat University (RBRU)
Thailand
apadcharoen@yahoo.com
Generalized asymptotically quasi-nonexpansive mapping
SP-iteration
CAT(0) space.
Article.18.pdf
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S. Dhompongsa, A. Kaewkhao, B. Panyanak, Lim's theorems for multivalued mappings in CAT(0) spaces, J. Math. Anal. Appl., 312 (2005), 478-487
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S. Dhompongsa, W. A. Kirk, B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal., 8 (2007), 35-45
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S. Dhompongsa, B. Panyanak , On \(\Delta\) -convergence theorem in CAT(0) spaces, Comput. Math. Appl., 56 (2008), 2572-2579
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H. Fukhar-ud-din, A. A. Domlo, A. R. Khan, Strong convergence of an implicit algorithm in CAT(0) spaces, Fixed Point Theory Appl., 2011 (2011), 1-11
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K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174
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S. H. Khan, M. Abbas, Strong and \(\Delta\) -convergence of some iterative schemes in CAT(0) spaces , Comput. Math. Appl., 61 (2011), 109-116
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W. A. Kirk, Fixed point theory in CAT(0) spaces and R-trees, Fixed Point Theory Appl., 4 (2004), 309-316
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W. A. Kirk, B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal., 68 (2008), 3689-3696
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P. Kumam, G. S. Saluja, H. K. Nashine, Convergence of modified S-iteration process for two asymptotically nonexpansive mappings in the intermediate sense in CAT(0) spaces, J. Inequalities Appl., 2014 (2014), 1-15
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T. C. Lim , Remarks on some fixed point theorems, Proc. Am. Math. Soc., 60 (1976), 179-182
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B. Nanjaras, B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl., 2010 (2010), 1-14
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W. Phuengrattana, S. Suantai, On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math., 235 (2011), 3006-3014
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A. Sahin, M. Basarir , On the strong and \(\Delta\) -convergence of SP-iteration on CAT(0) space, J. Inequal. Appl., 2013 (2013), 1-10
##[18]
P. Saipara, P. Chaipunya, Y. J. Cho, P. Kumam , On strong and \(\Delta\) -convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in CAT(\(\kappa\)) spaces , J. Nonlinear Sci. Appl., 8 (2015), 965-975
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J. F. Tang, S. S. Chang, H. W. Joseph Lee, C. K. Chan, Iterative Algorithm and \(\Delta\)-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Abstr. Appl. Anal., 2012 (2012), 1-11
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L. Wang, S. S. Chang, Z. Ma, Convergence theorems for total asymptotically nonexpansive non-self mappings in CAT(0) Spaces , J. Inequalities Appl., 2013 (2013), 1-10
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H. Y. Zhou, Y. J. Cho, M. Grabiec, Iterative process for generalized asymptotically nonexpansive mapping in Banach spaces, Panamer. Math. J., 13 (2003), 99-107
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H. Y. Zhou, G. L. Gao, G. T. Guo, Y. J. Cho, Some general convergence principles with application, Bull. Korean Math. Soc., 40 (2003), 351-363
]
An algorithm approach to maximal monotone operators and pseudo-contractions
An algorithm approach to maximal monotone operators and pseudo-contractions
en
en
The purpose of this article is to find the minimum norm solution of maximal monotone operators and
strict pseudo-contractions in Hilbert spaces. A parallel algorithm is constructed. Some analysis techniques
are used to show the convergence of the presented algorithm.
2136
2148
Xinhe
Zhu
Department of Mathematics
Tianjin Polytechnic University
China
zhumath@126.com
Zhangsong
Yao
School of Information Engineering
Nanjing Xiaozhuang University
China
yaozhsong@163.com
Abdelouahed
Hamdi
Department of Mathematics, Statistics and Physics, College of Arts and Sciences
Qatar University
Qatar
abhamdi@qu.edu.qa
Maximal monotone operator
strict pseudo-contractions
zero point
fixed point
minimum-norm.
Article.19.pdf
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H. H. Bauschke, J. M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Rev., 38 (1996), 367-426
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L. C. Ceng, Q. H. Ansari, J. C. Yao, Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem, Nonlinear Anal., 75 (2012), 2116-2125
##[3]
L. C. Ceng, S. M. Guu, J. C. Yao, Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense, J. Global Optim., 60 (2014), 617-634
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Y. Censor, Parallel application of block-iterative methods in medical imaging and radiation therapy, Math. Programming, 42 (1988), 307-325
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S. S. Chang, J. Kim, Y. J. Cho, J. Sim, Weak and strong convergence theorems of solutions to split feasibility problem for nonspreading type mapping in Hilbert spaces, Fixed Point Theory Appl., 2014 (2014), 1-12
##[6]
Y. J. Cho, Narin Petrot , Regularization method for Noor's variational inequality problem induced by a hemicontinuous monotone operator , Fixed Point Theory Appl., 2012 (2012), 1-13
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P. L. Combettes, Hilbertian convex feasibility problem: Convergence of projection methods , Appl. Math. Optim., 35 (1997), 311-330
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H. Pathak, Y. J. Cho , Strong convergence of a proximal-type algorithm for an occasionally pseudomonotone operator in Banach spaces, Fixed Point Theory Appl., 2012 (2012), 1-13
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H. K. Xu, Iterative Algorithms for Nonlinear Operators, J. London Math. Soc., 2 (2002), 240-256
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Y. Yao, R. P. Agarwal, M. Postolache, Y. C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl., 2014 (2014), 1-14
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H. Y. Zhou, Convergence theorems of fixed points for k-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal., 69 (2008), 456-462
]
Epidemic dynamics on a delayed multi-group heroin epidemic model with nonlinear incidence rate
Epidemic dynamics on a delayed multi-group heroin epidemic model with nonlinear incidence rate
en
en
For a multi-group Heroin epidemic model with nonlinear incidence rate and distributed delays, we
study some aspects of its global dynamics. By a rigorous analysis of the model, we establish that the
model demonstrates a sharp threshold property, completely determined by the values of \(\Re_0\): if \(\Re_0 \leq 1\),
then the drug-free equilibrium is globally asymptotically stable; if \(\Re_0 > 1\), then there exists a unique
endemic equilibrium and it is globally asymptotically stable. A matrix-theoretic method based on the
Perron eigenvector is used to prove the global asymptotic stability of the drug-free equilibrium and a graph-
theoretic method based on Kirchhoff's matrix tree theorem was used to guide the construction of Lyapunov
functionals for the global asymptotic stability of the endemic equilibrium.
2149
2160
Xianning
Liu
Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education), School of Mathematics and Statistics
Southwest University
China
liuxn@swu.edu.cn
Jinliang
Wang
School of Mathematical Science
Heilongjiang University
China
jinliangwang@hlju.edu.cn
Heroin epidemic model
multi-group
global stability
Lyapunov functionals.
Article.20.pdf
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A. Berman, R. J. Plemmons, Nonnegative matrices in the mathematical sciences, Academic Press, New York (1979)
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Fixed point theorems for generalized F-contractions in b-metric-like spaces
Fixed point theorems for generalized F-contractions in b-metric-like spaces
en
en
In this paper, we introduce some new F-contractions in b-metric-like spaces and investigate some fixed
point theorems for such F-contractions. Presented theorems generalize related results in the literature. An
example is also given to support our main result.
2161
2174
Chunfang
Chen
Department of Mathematics
Nanchang University
P. R. China
ccfygd@sina.com
Lei
Wen
Department of Mathematics
Nanchang University
P. R. China
newting@sina.cn
Jian
Dong
Department of Mathematics
Nanchang University
P. R. China
klgentle@sina.com
Yaqiong
Gu
Department of Mathematics
Nanchang University
P. R. China
924756324@qq.com
Fixed point
F-contraction
b-metric-like spaces.
Article.21.pdf
[
[1]
T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54 (2011), 2923-2927
##[2]
T. Abdeljawad, E. Karapinar, K. Taş, Existence and uniqueness of a commmon fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904
##[3]
J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized F-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-18
##[4]
M. A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl., 2013 (2013), 1-25
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H. H. Alsulami, E. Karapinar, H. Piri, Fixed points of generalized F-Suzuki type contraction in complete b-metric spaces, Discrete Dyn. Nat. Soc., 2015 (2015), 1-8
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H. H. Alsulami, E. Karapinar, H. Piri, Fixed points of modified F-contractive mappings in complete metric-like spaces, J. Funct. Spaces, 2015 (2015), 1-9
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A. Amini-Harandi , Metric-like spaces, partial metric spaces and fixed points , Fixed Point Theory Appl., 2012 (2012), 1-10
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T. V. An, L. Q. Tuyen, N. V. Dung , Stone-type theorem on b-metric spaces and applications, Topology Appl., 185/186 (2015), 50-64
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C. F. Chen, J. Dong, C. X. Zhu, Some fixed point theorems in b-metric-like spaces, Fixed Point Theory Appl., 2015 (2015), 1-10
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M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-Type, Filomat, 28 (2014), 715-722
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E. Karapinar, I. M. Erhan, A. Öztürk, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Model., 57 (2013), 2442-2448
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E. Karapinar, M. A. Kutbi, H. Piri, D. O'Regan, Fixed points of conditionally F-contractions in complete metric-like spaces, Fixed Point Theory Appl., 2015 (2015), 1-14
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M. A. Kutbi, E. Karapinar, J. Ahmad, A. Azam, Some fixed point results for multi-valued mappings in b-metric spaces, J. Inequal. Appl., 2014 (2014), 1-11
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S. G. Matthews, Partial metric topology, New York Acad. Sci., New York, 728 (1994), 183-197
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H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed point Theory Appl., 2014 (2014), 1-11
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D. Wardowski , Fixed points of a new type of contractive mappings in complete metric spaces , Fixed Point Theory Appl., 2012 (2012), 1-6
]
Fixed point theorems for cyclic mappings in quasi-partial b-metric spaces
Fixed point theorems for cyclic mappings in quasi-partial b-metric spaces
en
en
In this paper, we introduce the concepts of qpb-cyclic-Banach contraction mapping, qpb-cyclic-Kannan
mapping and qpb-cyclic \(\beta\)-quasi-contraction mapping and establish the existence and uniqueness of fixed
point theorems for these mappings in quasi-partial b-metric spaces. Some examples are presented to validate
our results.
2175
2189
Xiaoming
Fan
School of Mathematical Sciences
Harbin Normal University
P. R. China
fanxm093@163.com
Quasi-partial b-metric space
fixed point theorems
qpb-cyclic-Banach contraction mapping
qpb-cyclic-Kannan mapping
qpb-cyclic \(\beta\)-quasi-contraction mapping
Article.22.pdf
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[1]
A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 1-10
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
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N. Hussain, J. R. Roshan, V. Parvaneh, M. Abbas , Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications, J. Inequal. Appl., 2013 (2013), 1-21
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R. Kannan, Some results on fixed points - II, Amer. Math. Monthly, 76 (1969), 405-408
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E. Karapinar, I. M. Erhan, A. Öztürk, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Modelling, 57 (2013), 2442-2448
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E. Karapinar, I. M. Erhan, Best proximity point on different type contractions, Appl. Math. Inf. Sci., 5 (2011), 558-569
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C. Klin-eam, C. Suanoom, Dislocated quasi-b-metric spaces and fixed point theorems for cyclic contractions, Fixed Point Theory Appl., 2015 (2015), 1-12
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S. G. Matthews, Partial Metric Topology, Research Report 212, Department of Computer Science, University of Warwick (1992)
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S. G. Matthews, Partial metric topology, General Topology and its Applications, Ann. New York Acad. Sci., 728 (1992), 183-197
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A. Roldán-López-de-Hierro, E. Karapinar, M. De la Sen, Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-29
##[17]
S. Shukla , Partial b-metric spaces and fixed point theorems, Mediterr. J. Math., 11 (2014), 703-711
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C. Zhu, C. Chen, X. Zhang, Some results in quasi-b-metric-like spaces, J. Inequal. Appl., 2014 (2014), 1-8
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W. A. Wilson, On quasi-metric spaces, Amer. J. Math., 53 (1931), 675-684
]
On the solutions and periodicity of some nonlinear systems of difference equations
On the solutions and periodicity of some nonlinear systems of difference equations
en
en
We investigate the expressions of solutions and the periodicity nature of the following system of rational
difference equations of order four
\[x_{n+1 }= \frac{z_{n-3}}{ a_1 + b_1z_ny_{n-1}x_{n-2}z_{n-3}}, y_{n+1 }= \frac{x_{n-3}}{ a_2 + b_2x_nz_{n-1}y_{n-2}x_{n-3}},\]
\[z_{n+1 }= \frac{y_{n-3}}{ a_3 + b_3y_nx_{n-1}z_{n-2}y_{n-3}},\]
where the initial conditions\( x_{-3}; x_{-2}; x_{-1}; x_0, y_{-3}; y_{-2}; y_{-1}; y_0; z_{-3}; z_{-2}; z_{-1}\) and \(z_0\) are arbitrary real
numbers and \(a_1; b_1; a_2; b_2; a_3; b_3\) are integers.
2190
2207
M. M.
El-Dessoky
Faculty of Science, Mathematics Department
King AbdulAziz University
Saudi Arabia
dessokym@mans.edu.eg
System of difference equations
recursive sequences
stability
periodic solution
solution of difference equation.
Article.23.pdf
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[1]
R. P. Agarwal, Difference Equations and Inequalities, 1st edition, Marcel Dekker, New York, (1992), 2nd edition (2000)
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N. Battaloglu, C. Cinar, I. Yalçinkaya, The dynamics of the difference equation \(x_{n+1} = \frac{\alpha x_{n-k}}{ \beta+ \gamma x^p_{ n-(k+1)}}\), Ars Combin., 97 (2010), 281-288
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E. Camouzis, M. R. S. Kulenović, G. Ladas, O. Merino, Rational systems in the plane, J. Difference Equ. Appl., 15 (2009), 303-323
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C. Cinar , On the positive solutions of the difference equation system \(x_{n+1} = \frac{1}{ y_n} ; y_{n+1} = \frac{y_n}{ x_{n-1}y_{n-1}}\) , Appl. Math. Comput., 158 (2004), 303-305
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S. E. Das, M. Bayram, On a system of rational difference equations, World App. Sci. J., 10 (2010), 1306-1312
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E. M. Elabbasy, S. M. Eleissawy, Asymptotic behavior of two dimensional rational system of difference equations, Dyn. Contin. Discrete Impuls. Sys. Ser. B Appl. Algorithms, 20 (2013), 221-235
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S. Elaydi , An Introduction to Difference Equations , Undergrad. Texts Math., Springer, New York, NY, USA, 3rd edition (2005)
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M. M. El-Dessoky, On a solvable for some nonlinear systems of difference equations , J. Comput. Theor. Nanosci., 12 (2015), 3432-3442
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M. M. El-Dessoky, E. M. Elsayed , On a solution of system of three fractional difference equations , J. Comp. Anal. Appl., 19 (2015), 760-769
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M. M. El-Dessoky, M. Mansour, E. M. Elsayed, Solutions of some rational systems of difference equations, Util. Math., 92 (2013), 329-336
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E. M. Elsayed, Solutions of rational difference system of order two, Math. Comput. Model., 55 (2012), 378-384
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E. M. Elsayed, M. M. El-Dessoky, A. Alotaibi, On the solutions of a general system of difference equations, Discrete Dyn. Nat. Soc., 2012 (2012), 1-12
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E. M. Elsayed, M. M. El-Dessoky, E. O. Alzahrani , The form of the solution and dynamic of a rational recursive sequence, J. Comput. Anal. Appl., 17 (2014), 172-186
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E. M. Elsayed, M. Mansour, M. M. El-Dessoky, Solutions of fractional systems of difference equations , Ars Combin., 110 (2013), 469-479
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M. E. Erdoğan, C. Cinar, I. Yalçınkaya, On the dynamics of the recursive sequence, Comput. Math. Appl., 61 (2011), 533-537
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E. A. Grove, G. Ladas, L. C. McGrath, C. T. Teixeira, Existence and behavior of solutions of a rational system, Commun. Appl. Nonlinear Anal., 8 (2001), 1-25
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V. L. Kocić, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer, Dordrecht (1993)
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A. S. Kurbanli, On the behavior of solutions of the system of rational difference equations: \(x_{n+1} =\frac{ x_{n-1}}{ x_{n-1}y_{n }- 1} ; y_{n+1} =\frac{ y_{n-1}}{ y_{n-1}x_{n }- 1} \) , and \(x_{n+1} =\frac{ z_{n-1}}{ z_{n-1}y_{n }- 1} \) , Discrete Dyn. Nat. Soc., 2011 (2011), 1-12
##[23]
A. S. Kurbanli , On the behavior of solutions of the system of rational difference equations, Adv. Differ. Equ., 2011 (2011), 1-8
##[24]
A. S. Kurbanli, C. Cinar, I. Yalçinkaya, On the behavior of positive solutions of the system of rational difference equations \(x_{n+1} =\frac{ x_{n-1}}{ y_nx_{n-1} +1} ; y_{n+1} =\frac{ y_{n-1}}{x_{n } y_{n-1}+ 1} \), Math. Comput. Model., 53 (2011), 1261-1267
##[25]
K. Liu, Z. Wei, P. Li, W. Zhong, On the behavior of a system of rational difference equations \(x_{n+1} =\frac{ x_{n-1}}{ x_{n-1}y_{n }- 1} ; y_{n+1} =\frac{ y_{n-1}}{ y_{n-1}x_{n }- 1}, x_{n+1} =\frac{ 1}{ z_{n-1}x_{n }} \), Discrete Dyn. Nat. Soc., 2012 (2012), 1-9
##[26]
H. Ma, H. Feng, On positive solutions for the rational difference equation systems \(x_{n+1} = \frac{A}{ x_ny^2_n , y_{n+1}} =\frac{ By_n}{ x_{n-1}y_{n-1}}\) , Int. Schol. Res. Notices, 2014 (2014), 1-4
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M. Mansour, M. M. El-Dessoky, E. M. Elsayed, On the solution of rational systems of difference equations, J. Comp. Anal. Appl., 15 (2013), 967-976
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A. Y. Ozban, On the positive solutions of the system of rational difference equations \(x_{n+1} = \frac{1}{ y_{n-k}} ; y_{n+1} = \frac{y_n}{ x_{n-m}y_{n-m-k}}\), J. Math. Anal. Appl., 323 (2006), 26-32
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G. Papaschinopoulos, G. Ellina, K. B. Papadopoulos , Asymptotic behavior of the positive solutions of an exponential type system of difference equations, Appl. Math. Comput., 245 (2014), 181-190
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B. Sroysang, Dynamics of a system of rational higher-order difference equation, Discrete Dyn. Nat. Soc., 2013 (2013), 1-5
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S. Stević , On a solvable system of difference equations of fourth order, Appl. Math. Comput., 219 (2013), 5706-5716
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N. Touafek, On some fractional systems of difference equations , Iran. J. Math. Sci. Inform., 9 (2014), 73-86
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N. Touafek, E. M. Elsayed, On the solutions of systems of rational difference equations , Math. Comput. Model., 55 (2012), 1987-1997
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H. Yacine, Form and periodicity of solutions of some systems of higher-order difference equations, Math. Sci. Lett., 5 (2016), 79-84
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I. Yalcinkaya, C. Cinar, M. Atalay, On the solutions of systems of difference equations, Adv. Difference Equ., 2008 (2008), 1-9
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X. Yang, Y. Liu, S. Bai, On the system of high order rational difference equations\( x_n = \frac{a}{ y_{n-p}} , y_n = \frac{by_{n-p}}{ x_{n-q}y_{n-q}}\), Appl. Math. Comput., 171 (2005), 853-856
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Q. Zhang, J. Liu, Z. Luo, Dynamical behavior of a system of third-order rational difference equation, Discrete Dyn. Nat. Soc., 2015 (2015), 1-6
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Q. Zhang, W. Zhang, Y. Shao, J. Liu, On the system of high order rational difference equations, Int. Schol. Res. Notices, 2014 (2014), 1-5
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O. Zkan, A. S. Kurbanli , On a system of difference equation, Discrete Dyn. Nat. Soc., 2013 (2013), 1-7
]
Smoothness property of traveling wave solutions in a modified Kadomtsev--Petviashvili equation
Smoothness property of traveling wave solutions in a modified Kadomtsev--Petviashvili equation
en
en
In this paper, dynamical systems theory is applied to investigate the smooth property of traveling wave
solutions for a modified Kadomtsev{Petviashvili equation. The results of our study demonstrate that an
abundant of smooth traveling waves arise when their corresponding orbits have intersection points with the
singular straight line. In some conditions, exact parametric representations of these smooth waves in explicit
or implicit forms are obtained.
2208
2216
Lina
Zhang
Department of Mathematics
Huzhou University
P. R. China
zsdzln@126.com
Feng
Li
Department of Mathematics
Linyi University
P. R. China
lifeng@lyu.edu.cn
Xianglin
Han
Department of Mathematics
Huzhou University
P. R. China
xlhan@hutc.zj.cn
Bifurcation method
smooth wave solution
singular traveling wave system
mKP equation.
Article.24.pdf
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A. A. Andronov, E. A. Leontovich, I. I. Gordon, A. G. Mayer, Theory of bifurcations of dynamical systems on a plane, Wiley, New York (1973)
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C. W. Cao, Y. T. Wu, X. G. Geng, Relation between the Kadometsev-Petviashvili equation and the confocal involutive system, J. Math. Phys., 40 (1999), 3948-3970
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Y. F. Xu, Z. X. Dai , Bifurcations of exact traveling wave solutions for the (2 + 1)-dimensional mKP equation, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 22 (2012), 1-8
]
A coincident point principle for two weakly compatible mappings in partial S-metric spaces
A coincident point principle for two weakly compatible mappings in partial S-metric spaces
en
en
We show the existence of common fixed point and a coincident point for two weakly compatible self-
mappings defined on a complete partial S-metric space X, where the contraction in the assumption of the
main result has three control functions, \(\alpha,\psi,\phi\).
2217
2223
Nizar
Souayah
Department of Natural Sciences, Community College of Riyadh
King Saud University
Saudi Arabia
nizar.souayah@yahoo.fr
Nabil
Mlaiki
Department of General Sciences
Prince Sultan University
Saudi Arabia
nmlaiki2012@gmail.com
Functional analysis
partial S-metric space
common fixed point.
Article.25.pdf
[
[1]
M. Abbas, W. Shatanawi, T. Nazir, Common coupled coincidence and coupled fixed point of c-contractive mappings in generalized metric spaces, Thai J. Math., 13 (2015), 337-351
##[2]
T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54 (2011), 2923-2927
##[3]
T. Abdeljawad , Meir-Keeler alpha-contractive fixed and common fixed point theorems, Fixed Point Theory Appl., 2013 (2013), 1-10
##[4]
T. Abdeljawad, J. O. Alzabut, E. Mukheimer, Y. Zaidan , Best proximity points for cyclical contraction mappings with 0-boundedly compact decompositions, J. Comput. Anal. Appl., 15 (2013), 678-685
##[5]
T. Abdeljawad, K. Dayeh, N. Mlaiki , On fixed point generalizations to partial b-metric spaces, J. Comput. Anal. Appl., 19 (2015), 883-891
##[6]
T. Abdeljawad, E. Karapinar, K. Taş, A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63 (2012), 716-719
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The Borwein-Preiss variational principle for nonconvex countable systems of equilibrium problems
The Borwein-Preiss variational principle for nonconvex countable systems of equilibrium problems
en
en
The aim of the present paper, by using the Borwein-Preiss variational principle, we prove existence results
for countable systems of equilibrium problems. We establish some sufficient conditions which can guarantee
two existence theorems for countable systems of equilibrium problems on closed subsets of complete metric
spaces and on weakly compact subsets of real Banach spaces, respectively.
2224
2232
Somyot
Plubtieng
Department of Mathematics, Faculty of Science
Research center for Academic Excellence in Nonlinear Analysis and Optimization
Naresuan University
Naresuan University
Thailand
Somyotp@nu.ac.th
Thidaporn
Seangwattana
Research center for Academic Excellence in Nonlinear Analysis and Optimization
Naresuan University
seangwattana_t@hotmail.com
Borwein-Preiss variational principle
bifunction
complete metric space
equilibrium problems
gauge-type function
nonconvex.
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Nonexistence of solutions to a fractional differential boundary value problem
Nonexistence of solutions to a fractional differential boundary value problem
en
en
We investigate new results about Lyapunov-type inequality by considering a fractional boundary value
problem subject to mixed boundary conditions. We give a necessary condition for nonexistence of solutions
for a class of boundary value problems involving Riemann-Liouville fractional order. The order considered
here is \(3 < \alpha\leq 4\). The investigation is based on a construction of Green's function and on finding its
corresponding maximum value. In order to illustrate the result, we provide an application of Lyapunov-type
inequality for an eigenvalue problem and we show how the necessary condition of existence can be employed
to determine intervals for the real zeros of the Mittag-Leffler function.
2233
2243
Maysaa
Al-Qurashi
College of Sciences, Mathematics department
King Saud University
Saudi Arabia
maysaa@ksu.edu.sa
Lakhdar
Ragoub
Mathematics Department, College of Computers and Information Systems
Al Yamamah University
Saudi Arabia
radhkla@hotmail.com
Lyapunov's inequality
Green's function
Riemann-Liouville derivative
mixed boundary conditions.
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Common fixed point results for compatible-type mappings in multiplicative metric spaces
Common fixed point results for compatible-type mappings in multiplicative metric spaces
en
en
In this paper, we prove some common fixed point theorems for generalized contractive mappings satisfying
some conditions, that is, compatible and compatible-type mappings in multiplicative metric spaces. Our
results improve and generalize the corresponding results given in the literature. Moreover, we give some
examples to illustrate our main results.
2244
2257
Afrah A. N.
Abdou
Department of Mathematics
King Abdulaziz University
Saudi Arabia
aabdou@kau.edu.sa
Weak commutative mappings
multiplicative metric space
common fixed point.
Article.28.pdf
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H. H. Zheng, Y. J. Shen, F. Gu, A new common fixed point theorem for three pairs of self-maps satisfying common (E:A) property, J. Hangzhou Norm. Univ., Nat. Sci., 14 (2015), 77-81
]
Some results of common fixed point for four self-maps satisfying a new \(\Psi\)-contractive condition in partial metric spaces
Some results of common fixed point for four self-maps satisfying a new \(\Psi\)-contractive condition in partial metric spaces
en
en
In this paper, we prove some common fixed point theorems for two pairs of weakly compatible self-
maps satisfying a new \(\psi\) -contractive condition in the framework of a partial metric space. We also provide
illustrative examples in support of our new results. The results obtained in this paper differ from the recent
relative results in literature.
2258
2272
Hui-hui
Zheng
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
gufeng_99@163.com
Feng
Gu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
zhenghuihui910@sina.com
\(\psi\) -type contractive mapping
common fixed point
coincidence point
partial metric space
weakly compatible mappings.
Article.29.pdf
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[1]
T. Abdeljawad, Fixed points and generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54 (2011), 2923-2927
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T. Abdeljawad, E. Karapinar, K. Taş , Existence and uniqueness of a common fixed point on partial metric spaces , Appl. Math. Lett., 24 (2011), 1900-1904
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T. Abdeljawad, E. Karapinar, K. Taş, A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63 (2012), 716-719
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M. Akram, E. W. Shamaila, Fixed point results in partial metric spaces using generalized weak contractive conditions, J. Math. Comput. Sci., 12 (2014), 85-98
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I. Altun, Ö Acar, Fixed point theorems for weak contractions in the sense of Berinde on partial metric spaces, Topology Appl., 159 (2012), 2642-2648
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H. Aydi, Some fixed point results in ordered partial metric spaces, J. Nonlinear Sci. Appl., 4 (2011), 210-217
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H. Aydi , Fixed point theorems for generalized weakly contractive in ordered partial metric spaces, J. Nonlinear Anal. Optim. Theory Appl., 2 (2011), 269-284
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H. Aydi, M. Abbas, C. Vetroc , Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces , Topology Appl., 159 (2012), 3234-3242
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C. H. Chen, C. M. Chen, Fixed point results for Meir-Keeler-type \(\phi-\alpha\)-contractions on partial metric spaces, J. Inequal. Appl., 2013 (2013), 1-9
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C. Chen, C. Zhu, Fixed point theorems for weakly C-contractive mappings in partial metric spaces , Fixed Point Theory Appl., 2013 (2013), 1-16
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K. P. Chi, E. Karapinar, T. D. Thanha, A generalized contraction principle in partial metric spaces, Math. Comput. Modelling, 55 (2012), 1673-1681
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L. Ćirić, B. Samet, H. Aydi, C. Vetro, Common fixed point results of generalized contractions on partial metric spaces and application, Appl. Math. Comput., 218 (2011), 2398-2406
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A. Erduran, Z. Kadelburg, H. K. Nashine, C. Vetro , A fixed point theorem for (\(\varphi,L\))-weak contraction mappings on a partial metric space , J. Nonlinear Sci. Appl., 7 (2014), 196-204
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T. Nazir, M. Abbas, Common fixed points of two pairs of mappings satisfying (E.A)-property in partial metric spaces, J. Inequal. Appl., 2014 (2014), 1-12
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S. Oltra, O. Valero, Banach's fixed point theorem for partial metric spaces, Rend. Ist. Mat. Univ. Trieste, 36 (2004), 17-26
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V. L. Rosa, P. Vetro, Fixed points for Geraghty-contractions in partial metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 1-10
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W. Shatanawi, M. Postolache, Coincidence and fixed point results for generalized weak contractions in the sense of Berinde on partial metric spaces , Fixed Point Theory Appl., 2013 (2013), 1-17
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F. Vetro, S. Radenovic , Nonlinear w-quasi-contractions of Oirić-type in partial metric spaces , Appl. Math. Comput., 219 (2012), 1594-1600
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C. Vetro, F. Vetro, Common fixed points of mappings satisfying implicit relations in partial metric spaces , J. Nonlinear Sci. Appl., 6 (2013), 152-161
]
Common fixed point results of generalized almost rational contraction mappings with an application
Common fixed point results of generalized almost rational contraction mappings with an application
en
en
In this paper, we introduce the notion of generalized almost rational contraction with respect to a pair of
self mappings on a complete metric space. Several common fixed point results for such mappings are proved.
Our results extend and unify various results in the existing literature. An example and application to obtain
the existence of a common solution of the system of functional equations arising in dynamic programming
are also given in order to illustrate the effectiveness of the presented results.
2273
2288
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Huseyin
Isik
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science and Arts
Gazi University
Mus Alparslan University
Turkey
Turkey
isikhuseyin76@gmail.com
Mujahid
Abbas
Department of Mathematics
Department of Mathematics and Applied Mathematics
King Abdulaziz University
University Pretoria
Saudi Arabia
South Africa
mujahid.abbas@up.ac.za
Point of coincidence
common fixed point
cyclic admissible mappings
almost contractions
weakly compatible mappings
functional equations.
Article.30.pdf
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M. Abbas, B. Ali, C. Vetro , A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topology Appl., 160 (2013), 553-563
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M. Abbas, D. Doric, Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat, 24 (2010), 1-10
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R. P. Agarwal, N. Hussain, M. A. Taoudi , Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations , Abstr. Appl. Anal., 2012 (2012), 1-15
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A. H. Ansari, H. Isik, S. Radenović, Coupled fixed point theorems for contractive mappings involving new function classes and applications, Filomat, ( to appear. ), -
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H. Aydi, M. Abbas, C. Vetro, Common fixed points for multivalued generalized contractions on partial metric spaces, RACSAM, 108 (2014), 483-501
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N. Hussain, C. Vetro, F. Vetro, Fixed point results for \(\alpha\)-implicit contractions with application to integral equations, Nonlinear Anal. Model. Control, 21 (2016), 362-378
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H. Isik, B. Samet, C. Vetro, Cyclic admissible contraction and applications to functional equations in dynamic programming , Fixed Point Theory Appl., 2015 (2015), 1-19
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P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 1-19
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P. Salimi, N. Hussain, S. Shukla, S. Fathollahi, S. Radenovic, Fixed point results for cyclic \(\alpha,\psi,\phi\)-contractions with application to integral equations, J. Comput. Appl. Math., 290 (2015), 445-458
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B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings , Nonlinear Anal., 75 (2012), 2154-2165
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Y. Su , Contraction mapping principle with generalized altering distance function in ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl., 2014 (2014), 1-15
]
Some geometric properties of generalized modular sequence spaces defined by Zweier operator
Some geometric properties of generalized modular sequence spaces defined by Zweier operator
en
en
In this paper, the main purpose is to define generalized Cesàro sequence spaces by using the Zweier
operator and to investigate the property (H) and uniform Opial property in the spaces when they are
equipped with the Luxemburg norm.
2289
2297
Chanan
Sudsukh
Department of Mathematics Statistics and Computer Science, Faculty of Liberal Arts and Science
Kasetsart University, Kamphaeng-Saen Campus
Thailand
faaschs@ku.ac.th
Chirasak
Mongkolkeha
Department of Mathematics Statistics and Computer Science, Faculty of Liberal Arts and Science
Kasetsart University, Kamphaeng-Saen Campus
Thailand
faascsm@ku.ac.th
Generalized modular sequence spaces
Cesàro sequence spaces
property (H)
uniform Opial property
Zweier operator.
Article.31.pdf
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M. Et, M. Karakaş, M. Çinar, Some geometric properties of a new modular space defined by Zweier operator, Fixed Point Theory Appl., 2013 (2013), 1-10
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]
Schur-m power convexity for a mean of two variables with three parameters
Schur-m power convexity for a mean of two variables with three parameters
en
en
The Schur-m power convexity of a mean for two variables with three parameters is investigated and a
judging condition about the Schur-m power convexity of a mean for two variables with three parameters is
given.
2298
2304
Dongsheng
Wang
Basic courses department
Beijing Vocational College of Electronic Technology
China
wds000651225@sina.com
Chun-Ru
Fu
Applied college of science and technology
Beijing Union University
China
fuchunru2008@163.com
Huan-Nan
Shi
Department of Electronic Information, Teacher's College
Beijing Union University
P. R. China
sfthuannan@buu.com.cn;shihuannan2014@qq.com
Mean of two variables
Schur convexity
Schur geometric convexity
Schur harmonic convexity
Schur-m power convexity
majorization.
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]
Biomorphs via modified iterations
Biomorphs via modified iterations
en
en
The aim of this paper is to present some modifications of the biomorphs generation algorithm introduced
by Pickover in 1986. A biomorph stands for biological morphologies. It is obtained by a modified Julia set
generation algorithm. The biomorph algorithm can be used in the creation of diverse and complicated
forms resembling invertebrate organisms. In this paper the modifications of the biomorph algorithm in two
directions are proposed. The first one uses different types of iterations (Picard, Mann, Ishikawa). The second
one uses a sequence of parameters instead of one fixed parameter used in the original biomorph algorithm.
Biomorphs generated by the modified algorithm are essentially different in comparison to those obtained by
the standard biomorph algorithm, i.e., the algorithm with Picard iteration and one fixed constant.
2305
2315
Krzysztof
Gdawiec
Institute of Computer Science
University of Silesia
Poland
kgdawiec@ux2.math.us.edu.pl
Wieslaw
Kotarski
Institute of Computer Science
University of Silesia
Poland
kotarski@ux2.math.us.edu.pl
Agnieszka
Lisowska
Institute of Computer Science
University of Silesia
Poland
alisow@ux2.math.us.edu.pl
Biomorph
escape time algorithm
Mann iteration
Ishikawa iteration.
Article.33.pdf
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]
Dynamics of an almost periodic facultative mutualism model with time delays
Dynamics of an almost periodic facultative mutualism model with time delays
en
en
By using some new analytical techniques, modified inequalities and Mawhin's continuation theorem of
coincidence degree theory, some sufficient conditions for the existence of at least one positive almost periodic
solution of a kind of two-species model of facultative mutualism with time delays are obtained. Further, the
global asymptotic stability of the positive almost periodic solution of this model is also considered. Some
examples and numerical simulations are provided to illustrate the main results of this paper. Finally, a
conclusion is also given to discuss how the parameters of the system in
uence the existence and globally
asymptotic stability of positive almost periodic oscillations.
2316
2330
Zunguang
Guo
Department of Science
Taiyuan Institute of Technology
China
ruilang@aliyun.com
Can
Li
Department of Science
Taiyuan Institute of Technology
China
Almost periodic solution
coincidence degree
facultative mutualism
stability.
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]
Sharp estimates on the solutions to combined fractional boundary value problems on the half-line
Sharp estimates on the solutions to combined fractional boundary value problems on the half-line
en
en
We prove the existence and the uniqueness of a positive solution to the following combined fractional
boundary value problem on the half-line
\[
\begin{cases}
D^\alpha u(t)+a_1(t)u^{\sigma_1}+ a_2(t)u^{\sigma_2}=0,\,\,\,\,\, t\in (0,\infty), 1<\alpha<2\\
\lim_{t\rightarrow 0}t^{2-\alpha}u(t)=0,\lim_{t\rightarrow \infty}t^{1-\alpha}u(t) =0,
\end{cases}
\]
where \(D^\alpha\) is the standard Riemann{Liouville fractional derivative, \(\sigma_1; \sigma_2 \in (-1; 1)\), and \(a_1; a_2\) are non-negative continuous functions on (\(0,\infty\)), which may be singular at t = 0 and satisfying some convenient
assumptions related to the Karamata regular variation theory. We also give sharp estimates on such solution.
2331
2346
Imed
Bachar
College of Science, Mathematics Department
King Saud University
Saudi Arabia
abachar@ksu.edu.sa
Habib
Maagli
College of Sciences and Arts, Rabigh Campus, Department of Mathematics
King Abdulaziz University
Saudi Arabia
habib.maagli@fst.rnu.tn;abobaker@kau.edu.sa
Riemann-Liouville fractional derivative
Green's function
Karamata regular variation theory
positive solution
fixed point theorem.
Article.35.pdf
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R. P. Agarwal, M. Benchohra, S. Hamani, S. Pinelas, Boundary value problems for differential equations involving Riemann-Liouville fractional derivative on the half line, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 18 (2011), 235-244
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Fixed point theorems for generalized contraction mappings in multiplicative metric spaces
Fixed point theorems for generalized contraction mappings in multiplicative metric spaces
en
en
The purpose of this paper is to study and discuss the existence of common fixed points for weakly
compatible mappings satisfying the generalized contractiveness and the (CLR)-property. Our results improve
the corresponding results given in He et al. [X. He, M. Song, D. Chen, Fixed Point Theory Appl., 2014
(2014), 9 pages]. Moreover, we give some examples to illustrate for the main results.
2347
2363
Afrah A. N.
Abdou
Departement of Mathematics
King Abdulaziz University
Saudi Arabia
aabdou@kau.edu.sa
Multiplicative metric space
common fixed point
compatible mappings
weakly compatible mappings
the (CLR)-property.
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Existence and convergence theorems for the split quasi variational inequality problems on proximally smooth sets
Existence and convergence theorems for the split quasi variational inequality problems on proximally smooth sets
en
en
In this paper, we consider the split quasi variational inequality problems over a class of nonconvex sets,
as uniformly prox-regular sets. The sufficient conditions for the existence of solutions of such a problem
are provided. Furthermore, an iterative algorithm for finding a solution is constructed and its convergence
analysis are considered. The results in this paper improve and extend the variational inequality problems
which have been appeared in literature.
2364
2375
Jittiporn
Tangkhawiwetkul
Department of Mathematics, Faculty of Science and Technology
Pibulsongkram Rajabhat University
Thailand
j_suwannawit@hotmail.com
Narin
Petrot
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
narinp@nu.ac.th
Split quasi variational inequality
proximally smooth set
uniformly prox-regular set
Lipschitzian mapping
strongly monotone mapping.
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]
Anti-periodic solutions of Cohen-Grossberg shunting inhibitory cellular neural networks on time scales
Anti-periodic solutions of Cohen-Grossberg shunting inhibitory cellular neural networks on time scales
en
en
In this paper, Cohen-Grossberg shunting inhibitory cellular neural networks(CGSICNNs) on time scales
are investigated. Some sufficient conditions which ensure the existence and global exponential stability of
anti-periodic solutions for a class of CGSICNNs on time scales are established. Numerical simulations are
carried out to illustrate the theoretical findings. The results obtained in this paper are of great significance
in designs and applications of globally stable anti-periodic Cohen-Grossberg shunting inhibitory cellular
neural networks.
2376
2388
Changjin
Xu
Guizhou Key Laboratory of Economics System Simulation
Guizhou University of Finance and Economics
P. R. China
xcj403@126.com
Yicheng
Pang
School of Mathematics and Statistics
Guizhou University of Finance and Economics
P. R. China
ypanggy@outlook.com
Peiluan
Li
School of Mathematics and Statistics
Henan University of Science and Technology
P. R. China
lpllpl_lpl@163.com
Cohen-Grossberg shunting inhibitory cellular neural networks
anti-periodic solution
exponential stability
time scales.
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]
Degenerate q-Changhee polynomials
Degenerate q-Changhee polynomials
en
en
In this paper, we consider the degenerate q-Changhee numbers and polynomials. From the definition of
degenerate of q-Changhee polynomials, we derive some new interesting identities.
2389
2393
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Hyuck-In
Kwon
Department of Mathematics
Kwangwoon University
Republic of Korea
sura@kw.ac.kr
Jong Jin
Seo
Department of Applied Mathematics
Pukyong National University
Republic of Korea
seo2011@pknu.ac.kr
Euler polynomials
Changhee polynomials
fermionic p-adic q-integral
degenerate q-Changhee polynomials.
Article.39.pdf
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[1]
D. Ding, J. Yang , Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math., 20 (2010), 7-21
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L.-C. Jang, C. S. Ryoo, J. J. Seo, H. I. Kwon, Some properties of the twisted Changhee polynomials and their zeros, Appl. Math. Comput., 274 (2016), 169-177
##[3]
T. Kim, A note on p-adic q-integral on \(\mathbb{Z}_p\) associated with q-Euler numbers, Adv. Stud. Contemp. Math., 15 (2007), 133-137
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T. Kim, Note on the Euler numbers and polynomials, Adv. Stud. Contemp. Math., 17 (2008), 131-136
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T. Kim, A study on the q-Euler numbers and the fermionic q-integral of the product of several type q-Bernstein polynomials on \(\mathbb{Z}_p\), Adv. Stud. Contemp. Math., 23 (2013), 5-11
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]
Strong convergence of an iterative algorithm for accretive operators and nonexpansive mappings
Strong convergence of an iterative algorithm for accretive operators and nonexpansive mappings
en
en
In this paper, an iterative algorithm for finding a common point of the set of zeros of an accretive
operator and the set of fixed points of a nonexpansive mapping is considered in a uniformly convex Banach
space having a weakly continuous duality mapping. Under suitable control conditions, strong convergence
of the sequence generated by proposed algorithm to a common point of two sets is established. The main
theorems develop and complement the recent results announced by researchers in this area.
2394
2409
Jong Soo
Jung
Department of Mathematics
Dong-A University
Korea
jungjs@dau.ac.kr
Iterative algorithm
accretive operator
resolvent
zeros
nonexpansive mappings
fixed points
variational inequality
weakly continuous duality mapping
uniformly convex
contractive mapping
weakly contractive mapping.
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Q. Zhang, Y. Song, Halpern type proximal point algorithm of accretive operators, Nonlinear Anal., 75 (2012), 1859-1868
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The existence of Bayesian fuzzy equilibrium problems for a new general Bayesian abstract fuzzy economy model with differential private information
The existence of Bayesian fuzzy equilibrium problems for a new general Bayesian abstract fuzzy economy model with differential private information
en
en
In this work, we introduced a new Bayesian abstract fuzzy economy model with differential private
information and the Baysian fuzzy equilibrium problem, and we also prove the existence of the Baysian
fuzzy equilibrium problem for this new model. Our main results extended and improved the recent results
announced by many authors from the literature. The new concept of idea that the uncertainties characterize
the individual attribute of the choice or preference of the agents concerned in different economic actions.
2410
2418
Wiyada
Kumam
Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi (RMUTT)
Thailand
wiyada.kum@mail.rmutt.ac.th
Bayesian abstract fuzzy economy model
Bayesian fuzzy equilibrium problem
incomplete information
random fuzzy mappings
fuzzy mappings.
Article.41.pdf
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Application of new iterative transform method and modified fractional homotopy analysis transform method for fractional Fornberg-Whitham equation
Application of new iterative transform method and modified fractional homotopy analysis transform method for fractional Fornberg-Whitham equation
en
en
The main purpose of this paper is to present a new iterative transform method (NITM) and a modified
fractional homotopy analysis transform method (MFHATM) for time-fractional Fornberg-Whitham equation. The numerical results show that the MFHATM and NITM are very efficient and highly accurate for
nonlinear fractional differential equations.
2419
2433
Kangle
Wang
School of Mathematics and Statistics
XI'DIAN University
China
kangle83718@163.com
Sanyang
Liu
School of Mathematics and Statistics
XI'DIAN University
China
sanyangliu0819@126.com
Elzaki transform
iterative transform
homotopy analysis
fractional Fornberg-Whitham equation.
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Existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations with fractional integral boundary conditions
Existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations with fractional integral boundary conditions
en
en
This paper investigates the existence and uniqueness of solutions for a coupled system of nonlinear
fractional differential equations with Riemann-Liouville fractional integral boundary conditions. By applying
a variety of fixed point theorems, combining with a new inequality of fractional order form, some sufficient
conditions are established. Some examples are given to illustrate our results.
2434
2447
Haiyan
Zhang
School of Mathematics and Statistics
Suzhou University
China
liz.zhang@yeah.net
Yaohong
Li
School of Mathematics and Statistics
Suzhou University
P. R. China
liz.zhanghy@163.com
Wei
Lu
School of Mathematics and Statistics
Suzhou University
P. R. China
luwei6118@hotmail.com
Coupled system
fractional integral conditions
Remann-Liouville fractional derivative
fixed point theorem.
Article.43.pdf
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]
Coincidence best proximity point of \(F_g\)-weak contractive mappings in partially ordered metric spaces
Coincidence best proximity point of \(F_g\)-weak contractive mappings in partially ordered metric spaces
en
en
The aim of this paper is to present coincidence best proximity point results of \(F_g\)-weak contractive
mappings in partially ordered metric space. Some examples are presented to prove the validity of our
results.
2448
2457
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Mujahid
Abbas
Department of Mathematics
Department of Mathematics and Applied Mathematics
King Abdulaziz University
University of Pretoria
Saudi Arabia
South Africa
mujahid.abbas@up.ac.za
Azhar
Hussain
Department of Mathematics
University of Sargodha
Pakistan
hafiziqbal30@yahoo.com
Coincidence best proximity point
weak P-property
\(F_g\)-weak contraction mappings.
Article.44.pdf
[
[1]
M. Abbas, B. Ali, S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-11
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M. Abbas, A. Hussain, P. Kumam, A coincidence best proximity point problem in G-metric spaces, Abstr. Appl. Anal., 2015 (2015), 1-12
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M. Abbas, T. Nazir, S. Radenovic , Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., 24 (2011), 1520-1526
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M. Abbas, V. Rakočević, A. Hussain, Proximal cyclic contraction of perov type on regular cone metric space, J. Adv. Math. Stud., 9 (2016), 65-71
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A. Almeida, E. Karapinar, K. Sadarangani, A Note on Best Proximity Point Theorems under Weak P-Property , Abstr. Appl. Anal., 2014 (2014), 1-4
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N. Hussain, P. Salimi, Suzuki-Wardowski type fixed point theorems for \(\alpha\)-GF-contractions, Taiwanese J. Math., 18 (2014), 1879-1895
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M. Jleli, E. Karapinar, B. Samet , Best proximity points for generalized \(\alpha-\psi\)-proximal contractive type mappings, J. Appl. Math., 2013 (2013), 1-10
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M. Jleli, B. Samet, Best proximity points for \(\alpha-\psi\)-proximal contractive type mappings and applications, Bull. Sci. Math., 137 (2013), 977-995
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E. Karapinar , Best Proximity Points Of Cyclic Mappings, Appl. Math. Lett., 25 (2012), 1761-1766
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]
Best proximity points for cyclic Kannan-Chatterjea- Ćirić type contractions on metric-like spaces
Best proximity points for cyclic Kannan-Chatterjea- Ćirić type contractions on metric-like spaces
en
en
In this paper, we establish some best proximity results for Kannan-Chatterjea-Ćirić type contractions in
the setting of metric-like spaces. We also provide some concrete examples illustrating the obtained results.
2458
2466
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research
University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Abdelbasset
Felhi
Department of Mathematics, College of Sciences
King Faisal University
Saudi Arabia
afelhi@kfu.edu.sa
Metric-like
best proximity point
Kannan-Chatterjea-Ćirić contraction.
Article.45.pdf
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A. Abkar, M. Gabeleh, The existence of best proximity points for multivalued non-self-mappings, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 107 (2013), 319-325
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H. Aydi, A. Felhi, E. Karapinar, S. Sahmim, A Nadler-type fixed point theorem in metric-like spaces and applications, Accepted in Miskolc Math. Notes, (2015)
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H. Aydi, A. Felhi, S. Sahmim, Fixed points of multivalued nonself almost contractions in metric-like spaces, Math. Sci., 9 (2015), 103-108
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H. Aydi, E. Karapinar, Fixed point results for generalized \(\alpha-\psi\) -contractions in metric-like spaces and applications, Electron. J. Differential Equations, 2015 (2015), 1-15
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux quations intègrales, Fund. Math., 3 (1922), 133-181
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S. Basha, Best proximity point theorems, J. Approx. Theory, 163 (2011), 1772-1781
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E. Karapinar , Best proximity points of cyclic mappings, Appl. Math. Lett., 25 (2012), 1761-1766
##[17]
E. Karapinar , Best proximity points of Kannan type cyclic weak \(\phi\)-contractions in ordered metric spaces, An. Stiint. Univ. ''Ovidius'' Constanta Ser. Mat., 20 (2012), 51-63
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E. Karapinar, I. M. Erhan, Best proximity point on different type contractions, Appl. Math. Inf. Sci., 3 (2011), 342-353
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E. Karapinar, G. Petrusel, K. Tas, Best proximity point theorems for KT-types cyclic orbital contraction mappings, Fixed Point Theory, 13 (2012), 537-546
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J. Zhang, Y. Su, Q. Cheng , A note on ''A best proximity point theorem for Geraghty- contractions'', Fixed Point Theory Appl., 2013 (2013), 1-4
]
On the new fractional derivative and application to nonlinear Baggs and Freedman model
On the new fractional derivative and application to nonlinear Baggs and Freedman model
en
en
We presented the nonlinear Baggs and Freedman model with new fractional derivative. We derived the
special solution using an iterative method. The stability of the iterative method was presented using the
fixed point theory. The uniqueness of the special solution was presented in detail using some properties
of the inner product and the Hilbert space. We presented some numerical simulations to underpin the
effectiveness of the used derivative and semi-analytical method.
2467
2480
Abdon
Atangana
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences
University of the Free State
South Africa
abdonatangana@yahoo.fr
Ilknur
Koca
Department of Mathematics, Faculty of Sciences
Mehmet Akif Ersoy University
Turkey
ikoca@mehmetakif.edu.tr
Nonlinear Baggs and Freedman model
special solution
fixed point theorem
iterative method.
Article.46.pdf
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Functional inequalities in generalized quasi-Banach spaces
Functional inequalities in generalized quasi-Banach spaces
en
en
In this paper, we investigate the Hyers-Ulam stability of the following function inequalities
\[\|af(x) + bg(y) + ch(z)\| \leq \| K_p (\frac{ ax + by + cz}{k}) \| ;\]
\[\|af(x) + bg(y) + Kh(z)\| \leq \| K_p (\frac{ ax + by }{k} + z) \| ;\]
in generalized quasi-Banach spaces, where \(a; b; c;K\) are nonzero real numbers.
2481
2491
Ming
Fang
School of Mathematics and Statistics
School of Science
Northeast Normal University
Yanbian University
P. R. China
P. R. China
fangming@ybu.edu.cn
Gang
Lu
Shenyang University of Technology
P. R. China
lvgang1234@hanmail.net
Dong He
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Hyers-Ulam stability
additive functional inequality
generalized quasi-Banach space
additive mapping.
Article.47.pdf
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On common fixed points for (\(\alpha,\psi\))-contractions and generalized cyclic contractions in b-metric-like spaces and consequences
On common fixed points for (\(\alpha,\psi\))-contractions and generalized cyclic contractions in b-metric-like spaces and consequences
en
en
In this paper, using the concept of \(\alpha\)-admissible pairs of mappings, we prove several common fixed point
results in the setting of b-metric-like spaces. We also introduce the notion of generalized cyclic contraction
pairs and establish some common fixed results for such pairs in b-metric-like spaces. Some examples are
presented making effective the new concepts and results. Moreover, as consequences we prove some common
fixed point results for generalized contraction pairs in partially ordered b-metric-like spaces.
2492
2510
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research
University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Abdelbasset
Felhi
Department of Mathematics, College of Sciences
King Faisal University
Saudi Arabia
afelhi@kfu.edu.sa
Slah
Sahmim
Department of Mathematics. College of Sciences
King Faisal University
Saudi Arabia
ssahmim@kfu.edu.sa
Common fixed point
b-metric-like space
cyclic contraction
admissible mapping.
Article.48.pdf
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[1]
R. P. Agarwal, P. Kumam, W. Sintunavarat, PPF dependent fixed point theorems for an \(\alpha_c\)-admissible non-self mapping in the Razumikhin class, Fixed Point Theory Appl., 2013 (2013), 1-14
##[2]
M. A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl., 2013 (2013), 1-25
##[3]
M. U. Ali, T. Kamran, E. Karapinar, On (\(\alpha,\psi,\eta\))-contractive multivalued mappings, Fixed Point Theory Appl., 2014 (2014), 1-8
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H. Aydi, \(\alpha\)-implicit contractive pair of mappings on quasi b-metric spaces and application to integral equations, Accepted in J. Nonlinear Convex Anal., (2015)
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H. Aydi, M.-F. Bota, E. Karapinar, S. Moradi, A common fixed point for weak \(\phi\)-contractions on b-metric spaces, Fixed Point Theory, 13 (2012), 337-346
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H. Aydi, M. Jellali, E. Karapinar, Common fixed points for generalized \(\alpha\)-implicit contractions in partial metric spaces: Consequences and application, consequences and application, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 109 (2015), 367-384
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H. Aydi, E. Karapinar , A fixed point result for Boyd-Wong cyclic contractions in partial metric spaces , Int. J. Math. Math. Sci., 2012 (2012), 1-11
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H. Aydi, E. Karapinar, M.-F. Bota, S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-8
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H. Aydi, E. Karapinar, B. Samet , Fixed points for generalized (\(\alpha,\psi\) )-contractions on generalized metric spaces, J. Inequal. Appl., 2014 (2014), 1-16
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H. Aydi, C. Vetro, W. Sintunavarat, P. Kumam, Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-18
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M. Boriceanu, A. Petrusel, I. A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Int. J. Math. Stat., 6 (2010), 65-76
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Ch. Chen, J. Dong, Ch. Zhu, Some fixed point theorems in b-metric-like spaces, Fixed Point Theory Appl., 2015 (2015), 1-10
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M. Jleli, E. Karapinar, B. Samet , Best proximity points for generalized \(\alpha-\psi\) -proximal contractive type mappings, J. Appl. Math., 2013 (2013), 1-10
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M. Jleli, E. Karapinar, B. Samet, Fixed point results for \(\alpha-\psi_\lambda\) contractions on gauge spaces and applications, Abstr. Appl. Anal., 2013 (2013), 1-7
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E. Karapinar, Discussion on (\(\alpha,\psi\) )-contractions on generalized metric spaces, Abstr. Appl. Anal., 2014 (2014), 1-7
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E. Karapinar, P. Kumam, P. Salimi, On \(\alpha-\psi\)-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-12
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E. Karapinar, B. Samet, Generalized \(\alpha-\psi\)-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012), 1-17
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W. A. Kirk, P. S. Srinivasan, P. Veeramani , Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89
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P. Kumam, N. V. Dung, V. Th. Le Hang, Some equivalences between cone b-metric spaces and b-metric spaces, Abstr. Appl. Anal., 2013 (2013), 1-8
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B. Mohammadi, Sh. Rezapour, N. Shahzad, Some results on fixed points of \(\alpha-\psi\)-Ciric generalized multifunctions, Fixed Point Theory Appl., 2013 (2013), 1-10
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C. Mongkolkeha, P. Kumam, Best proximity point theorems for generalized cyclic contractions in ordered metric spaces, J. Optim. Theory Appl., 155 (2012), 215-226
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O. Popescu, Some new fixed point theorems for \(\alpha\)-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-12
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B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\) -contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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S. L. Singh, S. Czerwik, K. Krol, A. Singh, Coincidences and fixed points of hybrid contractions, Tamsui Oxf. J. Math. Sci., 24 (2008), 401-416
]
Some formulas for the generalized Apostol-type polynomials and numbers
Some formulas for the generalized Apostol-type polynomials and numbers
en
en
In this paper, we perform a further investigation for the unified family of the generalized Apostol-Bernoulli, Euler and Genocchi polynomials and numbers introduced by El-Desouky and Gomaa (2014).
By using the generating function methods and summation transform techniques, we establish some new
formulas for this family of polynomials and numbers, and give some illustrative special cases.
2511
2519
Wen-Kai
Shao
Department of Mathematical Teaching and Research
Yibin Vocational & Technical College
People's Republic of China
wksh_0@163.com
Yuan
He
Faculty of Science
Kunming University of Science and Technology
People's Republic of China
hyyhe@aliyun.com;hyyhe@outlook.com
Apostol-Bernoulli polynomials and numbers
Apostol-Euler polynomials and numbers
Apostol-Genocchi polynomials and numbers
combinatorial identities.
Article.49.pdf
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S. Araci, M. Acikgoz, E. Sen, New generalization of Eulerian polynomials and their applications, J. Anal. Number Theory, 2 (2014), 59-63
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R. Dere, Y. Simsek, H. M. Srivastava, A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra, J. Number Theory, 133 (2013), 3245-3263
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B. S. El-Desouky, R. S. Gomaa, A new unified family of generalized Apostol-Euler, Bernoulli and Genocchi polynomials, Appl. Math. Comput., 247 (2014), 695-702
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Y. He, S. Araci , Sums of products of Apostol-Bernoulli and Apostol-Euler polynomials, Adv. Difference Equ., 2014 (2014), 1-13
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Y. He, S. Araci, H. M. Srivastava, M. Acikgoz, Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials, Appl. Math. Comput., 262 (2015), 31-41
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D. S. Kim, T. Kim, q-Bernoulli polynomials and q-umbral calculus, Sci. China Math., 57 (2014), 1867-1874
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D. S. Kim, T. Kim, Umbral calculus associated with Bernoulli polynomials, J. Number Theory, 147 (2015), 871-882
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T. Kim, B. Lee, S. H. Lee, S. H. Rim, Some identities for the Frobenius-Euler numbers and polynomials, J. Comput. Anal. Appl., 15 (2013), 544-551
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L. M. Navas, F. J. Ruiz, J. L. Varona, Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials, Math. Comp., 81 (2011), 1707-1722
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N. E. Nörlund, Vorlesungen über Differenzenrechnung, Springer, Berlin (1924)
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M. A. Ozarslan, Unified Apostol-Bernoulli, Euler and Genocchi polynomials, Comput. Math. Appl., 62 (2011), 2452-2462
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H. Ozden, Y. Simsek, H. M. Srivastava, A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials, Comput. Math. Appl., 60 (2010), 2779-2787
]
An integrating factor approach to the Hyers-Ulam stability of a class of exact differential equations of second order
An integrating factor approach to the Hyers-Ulam stability of a class of exact differential equations of second order
en
en
Using the integrating factor method, this paper deals with the Hyers-Ulam stability of a class of exact
differential equations of second order. As a direct application of the main result, we also obtain the Hyers-Ulam stability of a special class of Cauchy-Euler equations of second order.
2520
2526
Yonghong
Shen
School of Mathematics and Statistics
Tianshui Normal University
P. R. China
shenyonghong2008@hotmail.com
Integrating factor method
Hyers-Ulam stability
exact differential equation
Cauchy-Euler equation.
Article.50.pdf
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M. R. Abdollahpour, A. Najati, Stability of linear differential equations of third order, Appl. Math. Lett., 24 (2011), 1827-1830
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S. András, J. J. Kolumbán, On the Ulam-Hyers stability of first order differential systems with nonlocal initial conditions, Nonlinar Anal., 82 (2013), 1-11
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G. Choi, S. M. Jung, Invariance of Hyers-Ulam stability of linear differential equations and its applications, Adv. Differ. Equ., 2015 (2015), 1-14
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D. S. Cîmpean, D. Popa, On the stability of the linear differential equation of higher order with constant coefficients, Appl. Math. Comput., 217 (2010), 4141-4146
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S. M. Jung, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett., 17 (2004), 1135-1140
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S. M. Jung, Hyers-Ulam stability of linear differential equations of first order (III), J. Math. Anal. Appl., 311 (2005), 139-146
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S. M. Jung, Hyers-Ulam stability of linear differential equations of first order, II, Appl. Math. Lett., 19 (2006), 854-858
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S. M. Jung, Hyers-Ulam stability of linear partial differential equations of first order, Appl. Math. Lett., 22 (2009), 70-74
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Y. Li, Y. Shen, Hyers-Ulam stability of linear differential equations of second order, Appl. Math. Lett., 23 (2010), 306-309
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T. Miura, S. E. Takahasi, H. Choda, On the Hyers-Ulam stability of real continuous function valued differentiable map, Tokyo J. Math., 24 (2001), 467-476
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C. Mortici, T. M. Rassias, S. M. Jung, The inhomogeneous Euler equation and its Hyers-Ulam stability, Appl. Math. Lett., 40 (2015), 23-28
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D. Popa, G. Pugna, Hyers-Ulam stability of Euler's differential equation, Results. Math., 2015 (2015), 1-9
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]
Global stability and stationary pattern of a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response
Global stability and stationary pattern of a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response
en
en
This paper is concerned with a diffusive prey-predator model with modified Leslie-Gower term and
Holling II functional response subject to the homogeneous Neumann boundary condition. Firstly, by upper
and lower solutions method, we prove the global asymptotic stability of the unique positive constant
steady state solution. Secondly, introducing the cross diffusion, we obtain the existence of non-constant
positive solutions. The results demonstrate that under certain conditions, even though the unique positive
constant steady state is globally asymptotically stable for the model with self-diffusion, the non-constant
positive steady states can exist due to the emergency of cross-diffusion, that is to say, cross-diffusion can
create stationary pattern. Finally, using the bifurcation theory and treating cross diffusion as a bifurcation
parameter, we obtain the existence of positive non-constant solutions.
2527
2540
Yan
Li
College of Science
China University of Petroleum (East China)
P. R. China
liyan@upc.edu.cn
Xinhong
Zhang
College of Science
China University of Petroleum (East China)
P. R. China
Bingchen
Liu
College of Science
China University of Petroleum (East China)
P. R. China
Prey-predator model
Leslie-Gower term
upper and lower solutions method
stationary pattern
bifurcation.
Article.51.pdf
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[1]
M. A. Alaoui, M. D. Okiye, Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, Appl. Math. Lett., 16 (2003), 1069-1075
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K. Ryu, I. Ahn, Positive steady-states for two interacting species models with linear self-cross diffusions, Discrete Contin. Dyn. Syst., 9 (2003), 1049-1061
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M. X. Wang, Non-constant positive steady states of the Sel’kov model, J. Differential Equations, 190 (2003), 600-620
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Fixed points of Bregman relatively nonexpansive mappings and solutions of variational inequality problems
Fixed points of Bregman relatively nonexpansive mappings and solutions of variational inequality problems
en
en
In this paper, we propose an iterative scheme for finding a common point of the fixed point set of a
Bregman relatively nonexpansive mapping and the solution set of a variational inequality problem for a
continuous monotone mapping. We prove a strong convergence theorem for the sequences produced by the
method. Our results improve and generalize various recent results.
2541
2552
Mohammed Ali
Alghamdi
Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Proff-malghamdi@hotmail.com
Naseer
Shahzad
Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
nshahzad@kau.edu.sa
Habtu
Zegeye
Department of Mathematics
University of Botswana
Botswana
habtuzh@yahoo.com
Bregman distance function
Bregman relatively nonexpansive mapping
fixed points of mappings
strong convergence
monotone mapping.
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On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis
On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis
en
en
The aim of this work is to introduce a new three step iteration scheme for approximating fixed points
of the nonlinear self mappings on a normed linear spaces satisfying Berinde contractive condition. We also
study the sufficient condition to prove that our iteration process is faster than the iteration processes of
Mann, Ishikawa and Agarwal, et al. Furthermore, we give two numerical examples which fixed points are
approximated by using MATLAB.
2553
2562
Wutiphol
Sintunavarat
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
wutiphol@mathstat.sci.tu.ac.th;poom_teun@hotmail.com
Ariana
Pitea
Department of Mathematics and Informatics
University Politehnica of Bucharest
Romania
arianapitea@yahoo.com
Picard iteration process
Mann iteration process
Ishikawa iteration process
rate of convergence
mean valued theorem.
Article.53.pdf
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Lightcone dual surfaces and hyperbolic dual surfaces of spacelike curves in de Sitter 3-space
Lightcone dual surfaces and hyperbolic dual surfaces of spacelike curves in de Sitter 3-space
en
en
In this paper, we consider the spacelike curves in de Sitter space and we investigate the singularities of
lightcone dual surfaces and hyperbolic dual surfaces of these spacelike curves in the framework of the theory
of Legendrian dualities between pseudo-spheres in Minkowski space. We classify the singularities of these
subjects and reveal the relationships between their singularities and geometric invariants of spacelike curves
under the action of the Lorentz group. As application and illustration of the main results, an example is
given.
2563
2576
Haiming
Liu
School of Mathematics
Mudanjiang Normal University
P. R. China
liuhm468@nenu.edu.cn
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
De Sitter space
Legendrian dualities
lightcone dual surfaces.
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Singularity analysis of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces
Singularity analysis of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces
en
en
This paper introduces the notions of pseudo null curves in Minkowski 4-space. Meanwhile, some geometrical characterizations and the singularities of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces,
which are generated by pseudo null curves, are considered in this paper.
2577
2589
Jianguo
Sun
School of Science
China University of Petroleum (east China)
China
sunjg616@163.com
Minkowski space
singularity
pseudo null hypersurfaces
pseudo hyperbolic hypersurfaces.
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]
Existence and viability for fractional differential equations with initial conditions at inner points
Existence and viability for fractional differential equations with initial conditions at inner points
en
en
This paper is concerned with nonlinear fractional differential equations with the Caputo derivative.
Existence results are obtained for terminal value problems and initial value problems with initial conditions
at inner points. It is also proved that the sufficient condition in order that a locally closed subset be a viable
domain is the tangency condition. As a corollary, the existence of positive solutions is obtained.
2590
2603
Qixiang
Dong
School of Mathematical Sciences
Yangzhou University
P. R. China
qxdongyz@outlook.com;qxdong@yzu.edu.cn
Fractional derivative
differential equation
initial value problem
viability
tangency condition.
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]
Approximation solvability of two nonlinear optimization problems involving monotone operators
Approximation solvability of two nonlinear optimization problems involving monotone operators
en
en
Fixed points of strict pseudocontractions and zero points of two monotone operators are investigated
based on a viscosity iterative method. A strong convergence theorem of common solutions is established in
the framework of Hilbert spaces. The results obtained in this paper improve and extend many corresponding
results announced recently.
2604
2614
Xiaomin
Xu
School of Economics and Management
North China Electric Power University
China
Yanxia
Lu
Department of Mathematics and physics
North China Electric Power university
China
Sun Young
Cho
Department of Mathematics
Gyeongsang National University
Korea
ooly61@hotmail.com
Iterative process
quasi-variational inclusion
nonexpansive mapping
fixed point.
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R. Ahmad, M. Dilshad , \(H(.; .)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces, J. Non-linear Sci. Appl., 5 (2012), 334-344
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Q. Yuan, Y. Zhang, Iterative common solutions of fixed point and variational inequality problems, J. Nonlinear Sci. Appl., 9 (2016), 1882-1890
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H. Zegeye, N. Shahzad, Strong convergence theorem for a common point of solution of variational inequality and fixed point problem, Adv. Fixed Point Theory, 2 (2012), 374-397
##[26]
M. Zhang, An algorithm for treating asymptotically strict pseudocontractions and monotone operators , Fixed Point Theory Appl., 2014 (2014), 1-14
]
Existence of solutions for nonlinear impulsive \(q_k\)-difference equations with first-order \(q_k\)-derivatives
Existence of solutions for nonlinear impulsive \(q_k\)-difference equations with first-order \(q_k\)-derivatives
en
en
In this paper, we study the nonlinear second-order impulsive \(q_k\)-difference equations with Sturm-Liouville
type, in which nonlinear team and impulsive teams are dependent on first-order \(q_k\)-derivatives. We obtain
the existence and uniqueness results of solutions for the problem by Banach's contraction mapping principle
and Schaefer's fixed point theorems. Finally, we give two examples to demonstrate the use of the main
results.
2615
2630
Changlong
Yu
College of Sciences
Hebei University of Science and Technology
P. R. China
changlongyu@126.com
Jufang
Wang
College of Sciences
Hebei University of Science and Technology
P. R. China
wangjufang1981@126.com
Yanping
Guo
College of Sciences
Hebei University of Science and Technology
P. R. China
guoyanping65@126.com
boundary value problem
\(q_k\)-derivative
\(q_k\)-integral
impulsive \(q_k\)-difference equation
fixed point theorem.
Article.58.pdf
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]
Scrambled sets of shift operators
Scrambled sets of shift operators
en
en
In this paper, some characterizations about orbit invariants, p-scrambled points and scrambled sets are
obtained. Applying these results solves a conjecture and two problems given in [X. Fu, Y. You, Nonlinear
Anal., 71 (2009), 2141-2152].
2631
2637
Xinxing
Wu
School of Sciences
Southwest Petroleum University
People's Republic of China
wuxinxing5201314@163.com
Guanrong
Chen
Department of Electronic Engineering
City University of Hong Kong
People's Republic of China
gchen@ee.cityu.edu.hk
Li-Yorke chaos
scrambled (chaotic) set
shift operator.
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Splitting methods for a convex feasibility problem in Hilbert spaces
Splitting methods for a convex feasibility problem in Hilbert spaces
en
en
In this paper, we investigate a convex feasibility problem based on a splitting method. Strong convergence
theorems are established without the aid of metric projections in the framework of real Hilbert spaces.
2638
2648
Yunpeng
Zhang
College of Electric Power
North China University of Water Resources and Electric Power
China
Yanling
Li
School of Mathematics and Information Sciences
North China University of Water Resources and Electric Power University
China
zhangypliyl@yeah.net
Equilibrium problem
monotone operator
feasibility problem
Hilbert space
projection.
Article.60.pdf
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[1]
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]
Sufficient conditions for pulse phenomena of nonlinear systems with state-dependent impulses
Sufficient conditions for pulse phenomena of nonlinear systems with state-dependent impulses
en
en
This paper is concerned with the problem of pulse phenomena of nonlinear systems with state-dependent
impulses. Some sufficient conditions which guarantee the absence or presence of pulse phenomena are derived
using impulsive control theory. Those results are more general than that given in some earlier references.
Two examples are given to illustrate the feasibility and advantage of the results.
2649
2657
Guixia
Sui
School of Mathematical Sciences
Primary Education
Shandong Normal University
Jinan Preschool Education College
P. R. China
P. R. China
Xiaodi
Li
School of Mathematical Sciences
Shandong Normal University
P. R. China
sodymath@163.com
Jinjun
Fan
School of Mathematical Sciences
Shandong Normal University
P. R. China
Donal
O'Regan
Department of Mathematics
National University of Ireland
Ireland
Pulse phenomena
nonlinear systems
state-dependent impulses
impulsive control theory.
Article.61.pdf
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X. Yang, J. Cao, J. Qiu, pth moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control, Neural Networks, 65 (2015), 80-91
]
On common best proximity points for generalized \(\alpha-\psi\)-proximal contractions
On common best proximity points for generalized \(\alpha-\psi\)-proximal contractions
en
en
We establish some common best proximity point results for generalized \(\alpha-\psi\)-proximal contractive
non-self mappings. We provide some concrete examples. We also derive some consequences on some best
proximity results on a metric space endowed with a graph.
2658
2670
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research
University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Abdelbasset
Felhi
Department of Mathematics and Statistics, College of Sciences
King Faisal University
Saudi Arabia
afelhi@kfu.edu.sa
Erdal
Karapinar
Department of Mathematics
Atilim University
Turkey
ekarapinar@atilim.edu.tr
Common best proximity point
common fixed point
\(\alpha-\psi\)-proximal contraction.
Article.62.pdf
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[1]
M. A. Al-Thagafi, N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Anal., 70 (2009), 3665-3671
##[2]
H. Aydi, \(\alpha\)-implicit contractive pair of mappings on quasi b-metric spaces and application to integral equations, Accepted in J. Nonlinear Convex Anal., (2015)
##[3]
H. Aydi, A. Felhi , Best proximity points for cyclic Kannan-Chatterjea- Ćirić type contractions on metric-like spaces, J. Nonlinear Sci. Appl., 9 (2016), 2458-2466
##[4]
A. A. Eldred, P. Veeramani , Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006
##[5]
A. Felhi, H. Aydi, Best proximity points and stability results for controlled proximal contractive set valued mappings, Fixed Point Theory Appl., 2016 (2016), 1-23
##[6]
M. R. Haddadi, Best proximity point iteration for nonexpensive mapping in Banach spaces, J. Nonlinear Sci. Appl., 7 (2014), 126-130
##[7]
M. Jleli, E. Karapinar, B. Samet, Best proximity points for generalized \(\alpha-\psi\)-proximal contractive type mappings, J. Appl. Math., 2013 (2013), 1-10
##[8]
S. Karpagam, S. Agrawal, Best proximity points theorems for cyclic Meir-Keeler contraction maps , Nonlinear Anal., 74 (2011), 1040-1046
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E. Karapinar, B. Samet , Generalized \(\alpha-\psi\) contractive type mappings and related fixed point theorems with applications , Abstr. Appl. Anal., 2012 (2012), 1-17
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W. K. Kim, S. Kum, K. H. Lee, On general best proximity pairs and equilibrium pairs in free abstract economies, Nonlinear Anal., 68 (2008), 2216-2227
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W. A. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim., 24 (2003), 851-862
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C. Mongkolkeha, P. Kumam, Best proximity point theorems for generalized cyclic contractions in ordered metric Spaces, J. Optim. Theory Appl., 155 (2012), 215-226
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H. K. Nashine, P. Kumam, C. Vetro , Best proximity point theorems for rational proximal contractions, Fixed Point Theory Appl., 2013 (2013), 1-11
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M. Omidvari, S. M. Vaezpour, R. Saadati , Best proximity point theorems for F-contractive non-self mappings, Miskolc Math. Notes, 15 (2014), 615-623
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V. S. Raj, A best proximity point theorems for weakly contractive non-self-mappings , Nonlinear Anal., 74 (2011), 4804-4808
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S. Sadiq Basha, Best proximity point theorems, J. Approx. Theory, 163 (2011), 1772-1781
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S. Sadiq Basha, P. Veeramani , Best proximity pairs and best approximations, Acta Sci. Math., 63 (1997), 289-300
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S. Sadiq Basha, P. Veeramani , Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory, 103 (2000), 119-129
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B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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W. Shatanawi , Best proximity point on nonlinear contractive condition, J. Physics, 435 (2013), 1-10
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W. Shatanawi, A. Pitea , Best proximity point and best proximity coupled point in a complete metric space with (P)-property, Filomat, 29 (2015), 63-74
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V. Vetrivel, P. Veeramani, P. Bhattacharyya, Some extensions of Fan's best approximation theorem, Numer. Funct. Anal. Optim., 13 (1992), 397-402
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J. Zhang, Y. Su, Q. Cheng, A note on 'A best proximity point theorem for Geraghty-contractions', Fixed Point Theory Appl., 2013 (2013), 1-4
]
Some random fixed point theorems in generalized convex metric space
Some random fixed point theorems in generalized convex metric space
en
en
In this paper, we consider a new random iteration process to approximate a common random fixed point
of a finite family of uniformly quasi-Lipschitzian random mappings in generalized convex metric spaces. Our
results presented in this paper extend and improve several recent results.
2671
2679
Chao
Wang
School of Mathematics and Statistics
Nanjing University of Information Science and Technology
P. R. China
wangchaosx@126.com
Shunjie
Li
School of Mathematics and Statistics
Nanjing University of Information Science and Technology
P. R. China
Lishunjie@nuist.edu.cn
Random iteration process
common random fixed point
uniformly quasi-Lipschitzian random mapping
generalized convex metric spaces.
Article.63.pdf
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[1]
I. Beg , Approximation of random fixed point in normed space, Nonlinear Anal., 51 (2002), 1363-1372
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A. T. Bharucha-Reid, Random integral equation, Academic Press, New York (1972)
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B. S. Choudhury, Random Mann iteration scheme, Appl. Math. Lett., 16 (2003), 93-96
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L. B. Ciric, Common fixed point theorems for a family of non-self mappings in convex metric spaces, Nonlinear Anal., 71 (2009), 1662-1669
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L. B. Ciric, J. S. Ume, M. S. Khan, On the convergence of the Ishikawa iterates to a common fixed point of two mappings, Arch. Math., 39 (2003), 123-127
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O. Hans, Random operator equation , 4th Berkeley Sympos. Math. Statist. and Prob., Univ. California Press, Berkeley, Calif., 2 (1961), 185-202
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A. R. Khan, M. A. Ahmed, Convergence of a general iterative scheme for a finite family of asymptotically quasi- nonexpansive mappings in convex metric spaces and applications, Comput. Math. Appl., 59 (2010), 2990-2995
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P. Kumam, S. Plubtieng, Some random fixed point theorems for non-self nonexpansive random operators, Turkish J. Math., 30 (2006), 359-372
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P. Kumam, S. Plubtieng, Some random fixed point theorems for random asymptotically regular operators, Demon-stratio Math., 42 (2009), 131-141
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Q. Liu, Iterative sequences for asymptotically quasi-nonexpansive mapping with error memeber , J. Math. Anal. Appl., 259 (2001), 18-24
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S. Plubtieng, P. Kumam, R. Wangkeeree, Approximation of a common random fixed point for a finite family of random operators, Int. J. Math. Math. Sci., 2007 (2007), 1-12
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P. L. Ramrez, Random fixed points of uniformly Lipschitzian mappings , Nonlinear Anal., 57 (2004), 23-34
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A. Spacek, Zufallige gleichungen, Czechoslovak Math. J., 5 (1955), 462-466
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K.-K. Tan, X.-Z. Yuan, Some random fixed point theorems, in: K.K.Tan (Ed.), Fixed point theory and applications, World Sci. Publ., River Edge, NJ, (1991), 334-345
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Y.-X. Tian, Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings, Comput. Math. Appl., 49 (2005), 1905-1912
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C. Wang, Some fixed point results for nonlinear mappings in convex metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 670-677
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C. Wang, L.-W. Liu, Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces , Nonlinear Anal., 70 (2009), 2067-2071
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I. Yildirim, S. H. Khan, Convergence theorems for common fixed points of asymptotically quasi-nonexpansive mappings in convex metric spaces, Appl. Math. Comput., 218 (2012), 4860-4866
]
A noncompactness measure for tvs-metric cone spaces and some applications
A noncompactness measure for tvs-metric cone spaces and some applications
en
en
We provide a natural topology for a cone metric space and a noncompactness measure is deffned for this
space, which enables us to extend existing results for mappings and set-valued mappings defined on classical
metric spaces. Moreover it is proved that the topology of any uniform topological space is generated by a
cone metric.
2680
2687
Raúl
Fierro
Instituto de Matemáticas
Pontificia Universidad Católica de Valparaíso
Chile
raul.fierro@pucv.cl;raul.fierro@uv.cl
Approximate and fixed points
noncompactness measure
uniform spaces
set-valued mapping
tvs-cone metric space.
Article.64.pdf
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]
Sharpened versions of Mitrinović-Adamović, Lazarević and Wilkers inequalities for trigonometric and hyperbolic functions
Sharpened versions of Mitrinović-Adamović, Lazarević and Wilkers inequalities for trigonometric and hyperbolic functions
en
en
In this paper, we establish new sharpened versions of Mitrinović-Adamović and Lazarević's inequalities.
Further, we provide an application of our results to the improvements of Wilker's inequality for trigonometric
and hyperbolic functions. We show that the coefficient assigned to each of these sharpened inequalities is
best possible.
2688
2696
Shan-He
Wu
Department of Mathematics
Longyan University
P. R. China
shanhewu@163.com
Shu-Guang
Li
Department of Mathematics
Longyan University
P. R. China
shuguanglily@sina.com
Mihály
Bencze
Department of Mathematics
University of Craiova
Romania
benczemihaly@gmail.com
Mitrinović-Adamović's inequality
Lazarević's inequality
Wilker's inequality
sharpening
best possible coefficient
trigonometric functions
hyperbolic functions.
Article.65.pdf
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[1]
C. P. Chen, Sharp Wilker- and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions, Integral Transforms Spec. Funct., 23 (2012), 865-873
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S. H. Wu, H. P. Yue, Y. P. Deng, Y. M. Chu, Several improvements of Mitrinović-Adamović and Lazarević's inequalities with applications to the sharpening of Wilker-type inequalities, J. Nonlinear Sci. Appl., 9 (2016), 1755-1765
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]
Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis
Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis
en
en
In the present paper, we introduce a method in order to obtain some new interesting relations and
identities of the Apostol-Bernoulli polynomials of higher order, which are derived from Bernoulli polynomial
basis. Finally, by utilizing this method, we also get formulas for the convolutions of Bernoulli and Euler
polynomials in terms of Apostol-Bernoulli polynomials of higher order.
2697
2704
Armen
Bagdasaryan
Department of Mathematics and Statistics
Institute for Control Sciences
American University of the Middle East
Russian Academy of Sciences
Kuwait
Russia
bagdasar@member.ams.org
Serkan
Araci
Department of Economics, Faculty of Economics, Administrative and Social Sciences
Hasan Kalyoncu University
Turkey
mtsrkn@hotmail.com
Mehmet
Acikgoz
Department of Mathematics, Faculty of Arts and Sciences
University of Gaziantep
Turkey
acikgoz@gantep.edu.tr
Yuan
He
Faculty of Science
Kunming University of Science and Technology
People's Republic of China
hyyhe@aliyun.com
Generating function
Bernoulli polynomials of higher order
Euler polynomials of higher order
Hermite polynomials
Apostol-Bernoulli polynomials of higher order
Apostol-Euler polynomials of higher order
identities.
Article.66.pdf
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[1]
S. Araci, M. Acikgoz, A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials, Adv. Stud. Contemp. Math., 22 (2012), 399-406
##[2]
S. Araci, E. Şen, M. Acikgoz, Theorems on Genocchi polynomials of higher order arising from Genocchi basis, Taiwanese J. Math., 18 (2014), 473-482
##[3]
A. G. Bagdasaryan, An elementary and real approach to values of the Riemann zeta function, Phys. Atom. Nucl., 73 (2010), 251-254
##[4]
J. Choi, P. J. Anderson, H. M. Srivastava, Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function, Appl. Math. Comput., 199 (2008), 723-737
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K. Dilcher, Sums of products of Bernoulli numbers, J. Number Theory, 60 (1996), 23-41
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Y. He, S. Araci, Sums of products of Apostol-Bernoulli and Apostol-Euler polynomials, Adv. Difference Equ., 2014 (2014), 1-13
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Y. He, C. Wang, Some formulae of products of the Apostol-Bernoulli and Apostol-Euler Polynomials, Discrete Dyn. Nat. Soc., 2012 (2012), 1-11
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A. Pintér, H. M. Srivastava, Addition theorems for the Appell polynomials and the associated classes of polynomial expansions, Aequationes Math., 85 (2013), 483-495
##[19]
F. Qi, Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind, Filomat, 28 (2014), 319-327
##[20]
H. M. Srivastava , Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci., 5 (2011), 390-444
##[21]
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]
Application of single step with three generalized hybrid points block method for solving third order ordinary differential equations
Application of single step with three generalized hybrid points block method for solving third order ordinary differential equations
en
en
This article considers the implementation of one step hybrid block method, three generalized hybrid
points developed in collocation interpolation approach. The basic numerical properties of the hybrid block
method was established and found to be convergent. The efficiency of the new method was confirmed on
some initial value problems and found to give better approximation than the existing methods in term of
error.
2705
2717
Zurni
Omar
Department of Mathematics, School of Quantitative Sciences, College of Art and Sciences
Univeristi Utara Malaysia
Malaysia
zurni@uum.edu.my
Rafat
Abdelrahim
Department of Mathematics, School of Quantitative Sciences, College of Art and Sciences
Univeristi Utara Malaysia
Malaysia
rafatshaab@yahoo.com
Hybrid method
block method
third order differential equation
single step
three generalized off step points.
Article.67.pdf
[
[1]
A. O. Adesanya, D. M. Udoh, A. M. Ajileye, A New Hybrid Block Method for Direct Solution of General Third Order Initial Value Problems of Ordinary Differential Equations, Int. J. Pure Appl. Math., 86 (2013), 365-375
##[2]
T. A. Anake , Continuous implicit hybrid one-step methods for the solution of initial value problems of general second-order ordinary differential equations, Covenant University, Nigeria (2011)
##[3]
T. A. Anake, D. O. Awoyemi, A. A. Adesanya, A one step method for the solution of general second order ordinary differential equations, Int. J. Sci. Tech., 4 (2012), 224-228
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D. O. Awoyemi , A P-stable Linear Multistep Method for Solving Third Order Ordinary Differential Equation, Int. J. Comput. Math., 80 (2003), 985-991
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K. M. Fasasi, A. O. Adesanya, S. O. Adee, One Step Continuous Hybrid Block Method for the Solution of \(y''' = f(x; y; y'; y'')\), J. nat. sci. res., 4 (2014), 55-62
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##[7]
S. N. Jator, Solving second order initial value problems by a hybrid multistep method without predictors, Appl. Math. Comput., 217 (2010), 4036-4046
##[8]
J. O. Kuboye, Z. Omar , Numerical Solution of Third Order Ordinary Differential Equations Using a Seven-Step Block Method, Int. J. Math. Anal., 9 (2015), 743-754
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##[10]
B. T. Olabode, An Accurate Scheme by Block Method for the Third Order Ordinary Differential Equations, Pacific j. sci. tech., 10 (2009), 136-142
##[11]
Z. Omar, J. O. Kuboye, Developing Block Method of order Seven for Solving Third Order Ordinary Differential Equations Directly Using Multistep Collocation Approach, Int. J. Appl. Math. Stat., 53 (2015), 165-173
##[12]
Z. Omar, M. Suleiman, Parallel R-Point Implicit Block Method for Solving Higher Order Ordinary Differential Equation Directly, J. Inf. Commun. Technol., 3 (2003), 53-66
##[13]
A. Sagir, An accurate computation of block hybrid method for solving stiff ordinary differential equations, IOSR J. Math., 4 (2012), 18-21
##[14]
L. K. Yap, F. Ismail, N. Senu, An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations, J. Appl. Math., 2014 (2014), 1-9
]
The asymptotic expansion for a class of non-linear singularly perturbed problems with optimal control
The asymptotic expansion for a class of non-linear singularly perturbed problems with optimal control
en
en
In this article, we discuss a class of three-dimensional non-linear singularly perturbed systems with
optimal control. Firstly, we confirm the existence of heteroclinic orbits connecting two equilibrium points
about their associated systems by necessary conditions of optimal control and functional theory. Secondly,
we study the asymptotic solutions of the singularly perturbed optimal control problems by the methods of
boundary layer functions and prove the existence of the smooth solutions and the uniform validity of the
asymptotic expansion. Finally, we cite an example to illustrate the result.
2718
2726
Han
Xu
School of Science
Linyi University
P. R. China
xuhan@lyu.edu.cn
Yinlai
Jin
School of Science
Linyi University
P. R. China
jinyinlai@sina.com
Boundary layer
Hamilton functions
heteroclinic orbit
optimal control.
Article.68.pdf
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[1]
V. F. Butuzov, A. B. Vasileva, The asymptotic theory of contrast structures, Automat. Rem. Contr., 3 (1997), 4-32
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##[5]
Y. Jin, X. Zhu, Z. Guo, X. Hu, L. Zhang, B. Ding, Bifurcations of non twisted heteroclinic loop with resonant eigenvalues, Sci. World. J., 2014 (2014), 1-8
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H. Xu, The two-order quasi-linear singular perturbed problems with infinite initial conditions, Appl. Mech. Materials, 353 (2013), 3248-3250
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H. Xu, Y. Jin, The asymptotic solutions for a class of nonlinear singular perturbed differential systems with time delays, Sci. World. J., 2014 (2014), 1-7
]
Stochastic Hopf Bifurcation of a novel finance chaotic system
Stochastic Hopf Bifurcation of a novel finance chaotic system
en
en
The paper investigated the existence and stability of the Stochastic Hopf Bifurcation for a novel finance
chaotic system with noise by the orthogonal polynomial approximation method, which reduces the stochastic
nonlinear dynamical system into its equal deterministic nonlinear dynamical system. And according to the
Gegenbauer polynomial approximation in Hilbert space, the financial system with random parameter can
be reduced into the deterministic equivalent system. The parameter condition to ensure the appearance of
Hopf bifurcation in this novel finance chaotic system is obtained by the Hopf bifurcation theorem. We show
that a supercritical Hopf bifurcation occurs at systems' unique equilibriums \(s_0\). In addition, the stability
and direction of the Hopf bifurcation is investigated by the calculation of the first Lyapunov coefficient.
And the critical value of stochastic Hopf bifurcation is determined by deterministic parameters and the
intensity of random parameter in stochastic system. Finally, the simulation results are presented to support
the analysis.
2727
2739
Jiangang
Zhang
Department of Mathematics
Lanzhou Jiaotong University
China
zhangjg7715776@126.com
Juan
Nan
Department of Mathematics
Lanzhou Jiaotong University
China
nanj5567346@126.com
Yandong
Chu
Department of Mathematics
Lanzhou Jiaotong University
China
cyd@mail.lzjtu.cn
Wenju
Du
School of Traffic and Transportation
Lanzhou Jiaotong University
China
duwenjuok@126.com
Xinlei
An
Department of Mathematics
Lanzhou Jiaotong University
China
anxin1983@163.com
Stochastic chaos
stability
stochastic Hopf bifurcation
Gegenbauer polynomial approximation.
Article.69.pdf
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G. L. Cai, J. Huang , A new finance chaotic attractor, Int. J. Nonlinear Sci., 3 (2007), 213-220
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A. A. Elsadany, Competition analysis of a triopoly game with bounded rationality, Chaos Solitons Fract., 45 (2012), 1343-1348
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G. Gambino, V. Sciacca, Intermittent and passivity based control strategies for a hyperchaotic system , Appl. Math. Comput., 221 (2013), 367-382
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Common fixed point theorem for subcompatible maps of type (\(\alpha\) ) in weak non-Archimedean intuitionistic fuzzy metric space
Common fixed point theorem for subcompatible maps of type (\(\alpha\) ) in weak non-Archimedean intuitionistic fuzzy metric space
en
en
In this paper, we introduce the definition of subcompatible maps and subcompatible maps of types (\(\alpha\))
and (\(\beta\)); which are respectively weaker than compatible maps and compatible maps of types (\(\alpha\)) and (\(\beta\)); in
weak non-Archimedean intuitionistic fuzzy metric spaces and give some examples and relationship between
these definitions. Thereafter, we prove common fixed point theorem for four subcompatible maps of type
(\(\alpha\)) in weak non-Archimedean intuitionistic fuzzy metric spaces.
2740
2752
Ferhan Sola
Erduran
Department of Mathematics, Faculty of Science
Gazi University
Turkey
ferhansola@gazi.edu.tr;ferhansola@yahoo.com
Cemil
Yildiz
Department of Mathematics, Faculty of Science
Gazi University
Turkey
cyildiz@gazi.edu.tr
Weak non-Archimedean intuitionistic fuzzy metric
subcompatible maps of types (\(\alpha\)) and (\(\beta\))
common fixed point.
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On common solutions gradient algorithms, strong convergence theorems and their applications
On common solutions gradient algorithms, strong convergence theorems and their applications
en
en
In this article, the common solutions of various nonlinear problems are investigated based on gradient
algorithms. We obtain the strong convergence of the gradient algorithm in the framework of Hilbert spaces.
We also give some applications to support the main results.
2753
2765
Qing
Yuan
Department of Mathematics
Linyi University
China
zjyuanq@yeah.net
Zunwei
Fu
Department of Mathematics
The University of Suwon
Korea
fuzunwei@eyou.com
Hilbert space
variational inequality
gradient algorithm
metric projection.
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[1]
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B. A. Bin Dehaish, X. Qin, A. Latif, O. H. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
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X. Qin, S. Y. Cho, L.Wang, A regularization method for treating zero points of the sum of two monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-10
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]
Modified forward-backward splitting methods for accretive operators in Banach spaces
Modified forward-backward splitting methods for accretive operators in Banach spaces
en
en
In this paper, we propose the modified splitting method for accretive operators in Banach spaces and
prove some strong convergence theorems of the proposed method under suitable conditions. Finally, we give
some applications to the minimization problems.
2766
2778
Nattawut
Pholasa
School of Science
University of Phayao
Thailand
nattawut_math@hotmail.com
Prasit
Cholamjiak
School of Science
University of Phayao
Thailand
prasitch2008@yahoo.com
Yeol Je
Cho
Department of Mathematics
Department of Mathematics
King Abdulaziz University
Education and the RINS Gyeongsang National University
Saudi Arabia
Korea
yjcho@gnu.ac.kr
Accretive operator
Banach space
splitting method
forward-backward splitting method.
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Dislocated quasi-b-metric spaces and fixed point theorems for cyclic weakly contractions
Dislocated quasi-b-metric spaces and fixed point theorems for cyclic weakly contractions
en
en
In this paper, we introduce the notions of type dqb-cyclic-weak Banach contraction, dqb-cyclic-\(\phi\)-
contraction and derive the existence of fixed point theorems on dislocated quasi-b-metric spaces. Our
main theorem extends and unifies existing results in the recent literature.
2779
2788
Cholatis
Suanoom
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
Cholatis.Suanoom@gmail.com
Chakkrid
Klin-eam
Department of Mathematics, Faculty of Science
Research Center for Academic Excellence in Mathematics
Naresuan University
Naresuan University
Thailand
Thailand
chakkridk@nu.ac.th
Suthep
Suantai
Department of Mathematics, Faculty of Science
Chiang Mai University
Thailand
scmti005@chiangmai.ac.th
Fixed points
dqb-cyclic-\(\phi\)-contraction
dislocated quasi-b-metric spaces
dqb-converges sequence theorems
dqb-Cauchy sequence theorems.
Article.73.pdf
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M. A. Alghamdi, N. Hussain, P. Salimi , Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl., 2013 (2013), 1-25
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]
Viscosity splitting methods for variational inclusion and fixed point problems in Hilbert spaces
Viscosity splitting methods for variational inclusion and fixed point problems in Hilbert spaces
en
en
In this paper, a viscosity splitting method is investigated for treating variational inclusion and fixed point
problems. Strong convergence theorems of common solutions are established in the framework of Hilbert
spaces. Applications are also provided to support the main results.
2789
2797
Xiaolong
Qin
Institute of Fundamental and Frontier Sciences
University of Electronic Science and Technology of China
China
qxlxajh@163.com
B. A. Bin
Dehaish
Department of mathematics, Faculty of Science
AL Faisaliah Campus, King Abdulaziz University
Saudi Arabia
bbendehaish@kau.edu.sa
Sun Young
Cho
Department of Mathematics
Gyeongsang National University
Korea
ooly61@hotmail.com
Convex feasibility problem
iterative process
monotone operator
fixed point
splitting algorithm.
Article.74.pdf
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B. A. Bin Dehaish, X. Qin, A. Latif, H. O. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
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S. Y. Cho, X. Qin, L. Wang, Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-15
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X. Qin, S. Y. Cho, L. Wnag, A regularization method for treating zero points of the sum of two monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-10
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X. Qin, S. Y. Cho, L. Wang, Convergence of splitting algorithms for the sum of two accretive operators with applications, Fixed Point Theory Appl., 2014 (2014), 1-12
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]
Some equivalence results for well-posedness of generalized hemivariational inequalities with clarkes generalized directional derivative
Some equivalence results for well-posedness of generalized hemivariational inequalities with clarkes generalized directional derivative
en
en
In this paper, we are devoted to exploring conditions of well-posedness for generalized hemivariational
inequalities with Clarke's generalized directional derivative in re
exive Banach spaces. By using some
equivalent formulations of the generalized hemivariational inequality with Clarke's generalized directional
derivative under different monotonicity assumptions, we establish two kinds of conditions under which the
strong \(\alpha\)-well-posedness and the weak \(\alpha\)-well-posedness for the generalized hemivariational inequality with
Clarke's generalized directional derivative are equivalent to the existence and uniqueness of its solution,
respectively.
2798
2812
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Information Management
Cheng Shiu University
Taiwan
simplexliou@hotmail.com
Ching-Feng
Wen
Center for Fundamental Science and Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
Generalized hemivariational inequality
Clarke's generalized directional derivative
contraction
well-posedness
relaxed monotonicity.
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The mixed \(L_p\)-dual affine surface area for multiple star bodies
The mixed \(L_p\)-dual affine surface area for multiple star bodies
en
en
Associated with the notion of the mixed \(L_p\)-affine surface area for multiple convex bodies for all real \(p
(p \neq -n)\) which was introduced by Ye, et al. [D. Ye, B. Zhu, J. Zhou, arXiv, 2013 (2013), 38 pages], we
define the concept of the mixed \(L_p\)-dual affine surface area for multiple star bodies for all real \(p (p \neq -n)\)
and establish its monotonicity inequalities and cyclic inequalities. Besides, the Brunn-Minkowski type
inequalities of the mixed \(L_p\)-dual affine surface area for multiple star bodies with two addition are also
presented.
2813
2822
Zhang
Ting
Department of Mathematics
China Three Gorges University
P. R. China
Wang
Weidong
Department of Mathematics
China Three Gorges University
P. R. China
wangwd722@163.com
Si
Lin
Department of Mathematics
Beijing Forestry University
P. R. China
\(L_p\)-affine surface area
\(L_p\)-dual affine surface area
multiple star bodies
Hölder inequality.
Article.76.pdf
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]
Generalized Newton Raphsons method free from second derivative
Generalized Newton Raphsons method free from second derivative
en
en
In this paper, we suggest and analyze two new iterative methods for solving nonlinear scalar equations
namely: the modified generalized Newton Raphson's method and generalized Newton Raphson's method
free from second derivative are having convergence of order six and five respectively. We also give several
examples to illustrate the efficiency of these methods.
2823
2831
Waqas
Nazeer
Division of Science and Technology
University of Education
Pakistan
nazeer.waqas@ue.edu.pk
Amir
Naseem
Department of Mathematics
Lahore Leads University
Pakistan
amir14514573@yahoo.com
Shin Min
Kang
Department of Mathematics and the RINS
Gyeongsang National University
South Korea
smkang@gnu.ac.kr
Young Chel
Kwun
Department of Mathematics
Dong-A University
South Korea
yckwun@dau.ac.kr
Nonlinear equations
Newton's method
generalized Newton Raphson's method
Halley's method
Article.77.pdf
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[1]
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A. Ali, M. S. Ahmad, W. Nazeer, M. Tanveer , New modified two-step Jungck iterative method for solving non- linear functional equations , Sci. Int. (Lahore), 27 (2015), 2959-2963
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A. Ali, M. S. Ahmad, M. Tanveer, Q. Mehmood, W. Nazeer , Modified two-step fixed point iterative method for solving non-linear functional equations, Sci. Int. (Lahore), 27 (2015), 1737-1739
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J. Kou, The improvement of modified Newton's method, Appl. Math. Comput., 189 (2007), 602-609
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W. Nazeer, S. M. Kang, M. Tanveer, Modified Abbasbandy's Method for Solving Nonlinear Functions with Con- vergence of Order Six, Int. J. Math. Anal., 9 (2015), 2011-2019
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]
Multi-level and antipodal labelings for certain classes of circulant graphs
Multi-level and antipodal labelings for certain classes of circulant graphs
en
en
A radio k-labeling c of a graph G is a mapping \(c : V (G) \rightarrow Z^+\cup \{0\}\) such that \(d(u; v)+|c(u)-c(v)| \geq k+1\)
for every two distinct vertices u and v of G, where d(u; v) is the distance between any two vertices u and v
of G. The span of a radio k-labeling c is denoted by sp(c) and defined as \(\max\{|c(u) - c(v)| : u; v \in V (G)\}\).
The radio labeling is a radio k-labeling when \(k = diam(G)\). In other words, a radio labeling is a one-to-one
function f from \(V (G)\) to \(Z^+ \cup \{0\}\) such that \(|c(u) - c(v)| \geq diam(G) + 1 - d(u; v)\) for any pair of vertices
u, v in G. The radio number of G expressed by rn(G), is the lowest span taken over all radio labelings
of the graph. For \(k = diam(G) - 1\), a radio k- labeling is called a radio antipodal labeling. An antipodal
labeling for a graph G is a function \(c : V (G) \rightarrow \{0; 1; 2; ... \}\) such that \(d(u; v) + |c(u) - c(v)| \geq diam(G)\)
for all \(u; v \in V (G)\). The radio antipodal number for G denoted by an(G), is the minimum span of an
antipodal labeling admitted by G. In this paper, we investigate the exact value of the radio number and
radio antipodal number for the circulant graphs \(G(4mk + 2m; \{1; 2m\}),\) when \(m \geq 3\) is odd. Furthermore,
we also determine the lower bound of the radio number for the circulant graphs \(G(4mk + 2m; \{1; 2m\}),\)
when \(m \geq 2\) is even.
2832
2845
Shin Min
Kang
Department of Mathematics and the RINS
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Saima
Nazeer
Department of Mathematics
Lahore College for Women University
Pakistan
saimanazeer123@yahoo.com
Imrana
Kousar
Department of Mathematics
Lahore College for Women University
Pakistan
imrana.kousar@hotmail.com
Waqas
Nazeer
Division of Science and Technology
University of Education
Pakistan
nazeer.waqas@ue.edu.pk
Young Chel
Kwun
Department of Mathematics
Dong-A University
Korea
yckwun@dau.ac.kr
Diameter
radio number
radio antipodal number
circulant graphs.
Article.78.pdf
[
[1]
G. Chartrand, D. Erwin, P. Zhang, Radio antipodal colourings of cycles, Cong. Numer., 144 (2000), 129-141
##[2]
G. Chartrand, D. Erwin, P. Zhang, F. Harary, Radio labelings of graphs, Bull. Inst. Combin. Appl., 33 (2001), 77-85
##[3]
G. Chartrand, L. Nebeský, P. Zhang, Radio k-colorings of paths, Discuss. Math. Graph Theory, 24 (2004), 5-21
##[4]
W. K. Hale , Frequency assignment: theory and application, Proc. IEEE, 68 (1980), 1497-1514
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J. S. Juan, D. D. F. Liu, Antipodal labelings for cycles, Ars Combin., 103 (2012), 81-96
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C. Y. Jung, W. Nazeer, S. Nazeer, A. Rafiq, S. M. Kang, Radio number for cross product \(P_n(P_2)\), Int. J. Pure Appl. Math., 97 (2014), 515-525
##[7]
M. Kchikech, R. Khenoufa, O. Togni, Radio k-labelings for Cartesian products of graphs, Discuss. Math. Graph Theory, 28 (2008), 165-178
##[8]
R. Khennoufa, O. Togni , The radio antipodal and radio numbers of the hypercube, Ars Combin., 102 (2011), 447-461
##[9]
I. Kousar, S. Nazeer, W. Nazeer, Multilevel distance labelings for generalized petersend graph P(n; 3) , Sci. Int. (Lahore), 27 (2015), 1767-1777
##[10]
D. D. F. Liu, M. Xie, Radio number for square cycles, Congr. Numer., 169 (2004), 105-125
##[11]
D. D. F. Liu, X. Zhu, Multilevel distance labelings for paths and cycles, SIAM J. Discrete Math., 19 (2005), 610-621
##[12]
S. Nazeer, I. Kousar, W. Nazeer, Multilevel distance labeling for the graphs having diameter equal to diameter of cycle, Sci. Int. (Lahore), 26 (2014), 519-525
##[13]
S. Nazeer, I. Kousar, W. Nazeer, Radio number for prism related graphs \(D^*_n\) , Sci. Int. (Lahore), 26 (2014), 551-555
##[14]
S. Nazeer, I. Kousar, W. Nazeer, Radio and radio antipodal labelings for circulant graphs G(4k+2; 1; 2), J. Appl. Math. Inform., 33 (2015), 173-183
##[15]
M. T. Rahim, I. Tomescu , Multi-level distance labelings for helm graphs, Ars Combin., 104 (2012), 513-523
]
On the approximation of a convex body by its radial mean bodies
On the approximation of a convex body by its radial mean bodies
en
en
In this paper, we consider the approximation problem on the volume of a convex body \(K\) in \(\mathbb{R}^n\) by those
of its radial mean bodies \(R_pK\): Specifically, we establish the identity
\[\lim_{p\rightarrow \infty}\frac{P}{\log P}(1-2^{-n}\frac{|R_P(K)|}{|K|})=\frac{n(n+1)}{2};\]
when K is an ellipsoid in \(\mathbb{R}^n\).
2846
2856
Lvzhou
Zheng
School of Mathematics and Statistics
Hubei Normal University
P. R. China
oasiszlz@sina.com
Convex body
radial mean body
difference body
restricted chord projection function.
Article.79.pdf
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G. Paouris, M. E. Werner, On the approximation of a polytope by its dual Lp-centroid bodies, Indiana Univ. Math. J., 62 (2013), 235-248
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G. Xiong, W. Cheung, Chord power integrals and radial mean bodies, J. Math. Anal. Appl., 342 (2008), 629-637
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]
Differential equations for Changhee polynomials and their applications
Differential equations for Changhee polynomials and their applications
en
en
Recently, the non-linear Changhee differential equations were introduced by Kim and Kim [T. Kim, D.
S. Kim, Russ. J. Math. Phys., 23 (2016), 1-5] and these differential equations turned out to be very useful
for studying special polynomials and mathematical physics. Some interesting identities and properties
of Changhee polynomials can also be derived from umbral calculus (see [D. S. Kim, T. Kim, J. J. Seo,
Adv. Studies Theor. Phys., 7 (2013), 993-1003]). In this paper, we consider differential equations arising
from Changhee polynomials and derive some new and explicit formulae and identities from our differential
equations.
2857
2864
Taekyun
Kim
Department of Mathematics
Kwangwoon University
Republic of Korea
tkkim@kw.ac.kr
Dmitry V.
Dolgy
Institute of Mathematics and Computer Science
Far Eastern Federal University
Russia
dvdolgy@gmail.com
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Jong Jin
Seo
Department of Applied Mathematics
Pukyong National University
Republic of Korea
seo2011@pknu.ac.kr
Changhee polynomials
differential equations.
Article.80.pdf
[
[1]
A. Bayad, J. Chikhi , Apostol-Euler polynomials and asymptotics for negative binomial reciprocals, Adv. Stud. Contemp. Math., 24 (2014), 33-37
##[2]
L.-C. Jang, C. S. Ryoo, J. J. Seo, H. I. kwon, Some properties of the twisted Changhee polynomials and their zeros, Appl. Math. Comput., 274 (2016), 169-177
##[3]
T. Kim, Non-Archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys., 10 (2003), 91-98
##[4]
D. S. Kim, T. Kim, A note on Boole polynomials, Integral Transforms Spec. Funct., 25 (2014), 627-633
##[5]
D. S. Kim, T. Kim, Some identities of Korobov-type polynomials associated with p-adic integrals on \(\mathbb{Z}_p\), Adv. Difference Equ., 2015 (2015), 1-13
##[6]
T. Kim, D. S. Kim , A note on non-linear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 1-5
##[7]
D. S. Kim, T. Kim, T. Komatsu, S.-H. Lee, Barnes-type Daehee of the first kind and poly-Cauchy of the first kind mixed-type polynomials, Adv. Difference Equ., 2014 (2014), 1-22
##[8]
D. S. Kim, T. Kim, J. J. Seo, A Note on Changhee Polynomials and Numbers, Adv. Studies Theor. Phys., 7 (2013), 993-1003
##[9]
T. Kim, T. Mansour , Umbral calculus associated with Frobenius-type Eulerian polynomials, Russ. J. Math. Phys., 21 (2014), 484-493
##[10]
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S.-H. Rim, J.-W. Park, S.-S. Pyo, J. Kwon, The n-th twisted Changhee polynomials and numbers, Bull. Korean Math. Soc., 52 (2015), 741-749
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G. Y. Sohn, J. K. Kwon, A note on twisted Changhee polynomials and numbers with weight, Appl. Math. Sci., 9 (2015), 1517-1525
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N. L. Wang, H. Li , Some identities on the Higher-order Daehee and Changhee Numbers, Pure Appl. Math. J., 4 (2015), 33-37
]
Strong convergence analysis of a monotone projection algorithm in a Banach space
Strong convergence analysis of a monotone projection algorithm in a Banach space
en
en
An uncountable infinite family of generalized asymptotically quasi-\(\phi\)-nonexpansive mappings and bifunctions are investigated based on a monotone projection algorithm in this article. Strong convergence of the
algorithm is obtained in the framework of Banach spaces.
2865
2874
Xiaolong
Qin
Institute of Fundamental and Frontier Sciences
University of Electronic Science and Technology of China
China
qxlxajh@163.com
B. A. Bin
Dehaish
Department of mathematics
Faculty of Science-AL Faisaliah Campus, King Abdulaziz University
Saudi Arabia
bbendehaish@kau.edu.sa
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Sun Young
Cho
Department of Mathematics
Gyeongsang National University
Korea
ooly61@hotmail.com
Quasi-\(\phi\)-nonexpansive mapping
equilibrium problem
fixed point
projection
variational inequality.
Article.81.pdf
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[1]
R. P. Agarwal, Y. J. Cho, X. Qin, Generalized projection algorithms for nonlinear operators, Numer. Funct. Anal. Optim., 28 (2007), 1197-1215
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R. P. Agarwal, X. Qin, S. M. Kang, An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings, Fixed Point Theory Appl., 2011 (2011), 1-17
##[3]
Y. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, in: A.G. Kartsatos (Ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Marcel Dekker, New York (1996)
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B. A. Bin Dehaish, A. Latif, H. Bakodah, X. Qin, A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2013 (2013), 1-14
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B. A. Bin Dehaish, X. Qin, A. Latif, H. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
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B. Liu, C. Zhang, Strong convergence theorems for equilibrium problems and quasi-\(\phi\)-nonexpansive mappings, Nonlinear Funct. Anal. Appl., 16 (2011), 365-385
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X. Qin, R. P. Agarwal, S. Y. Cho, S. M. Kang, Convergence of algorithms for fixed points of generalized asymptotically quasi-\(\phi\)-nonexpansive mappings with applications, Fixed Point Theory Appl., 2012 (2012), 1-20
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X. Qin, B. A. Bin Dehaish, S. Y. Cho , Viscosity splitting methods for variational inclusion and fixed point problems in Hilbert spaces, J. Nonlinear Sci. Appl., 9 (2016), 2789-2797
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]
Legendrian dualities between spherical indicatrixes of curves and surfaces according to Bishop frame
Legendrian dualities between spherical indicatrixes of curves and surfaces according to Bishop frame
en
en
Legendrian dualities between spherical indicatrixes of curves in Euclidean 3-space are investigated by
using the theory of Legendrian duality. Moreover, the singularities of the ruled surfaces according to Bishop
frame which are deeply related to space curves are classified from the viewpoints of wave fronts. We also
give some more detail descriptions on the conditions of those singularities.
2875
2887
Haiming
Liu
School of Mathematics
Mudanjiang Normal University
P. R. China
liuhm468@nenu.edu.cn
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Ruled surfaces
Bishop frame
Legendrian dualities
singularity theory.
Article.82.pdf
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[1]
R. L. Bishop, There is more than one way to frame a curve , Amer. Math. Monthly, 82 (1975), 246-251
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J. W. Bruce, P. J. Giblin, Curves and Singularities, Cambridge University Press, Cambridge (1992)
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B. Bükcü, M. K. Karacan, Special Bishop motion and Bishop Darboux rotation axis of the space curve, J. Dyn. Syst. Geom. Theor., 6 (2008), 27-34
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L. Chen, Q. Han, D. Pei, W. Sun , The singularities of null surfaces in anti de Sitter 3-space , J. Math. Anal. Appl., 366 (2010), 256-265
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N. Clauvelin, W. K. Olson, I. Tobias, Characterization of the geometry and topology of DNA pictured as a discrete collection of atoms, J. Chem. Theory Comput., 8 (2012), 1092-1107
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C. Y. Han , Nonexistence of rational rotation-minimizing frames on cubic curves , Comput. Aided Geom. Design, 25 (2008), 298-304
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M. K. Karacan, B. Bükcü, An alternative moving frame for tubular surfaces around timelike curves in the Minkowski 3-space , Balkan J. Geom. Appl., 12 (2007), 73-80
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Ş. Kiliçouğlu, H. Hacaısalihoğlu, On the ruled surfaces whose frame is the Bishop frame in the Euclidean 3-space , Int. Electron. J. Geom., 6 (2013), 110-117
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T. Körpinar, E. Turhan, On characterization of B-canal surfaces in terms of biharmonic B-slant helices according to Bishop frame in Heisenberg group Heis3, J. Math. Anal. Appl., 382 (2011), 57-65
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H. Liu, D. Pei , Singularities of a space curve according to the relatively parallel adapted frame and its visualization, Math. Probl. Eng., 2013 (2013), 1-12
##[12]
H. Liu, D. Pei, Cusps of Bishop spherical indicatrixes and their visualizations , Math. Probl. Eng., 2013 (2013), 1-11
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H. Liu, D. Pei , Lightcone dual surfaces and hyperbolic dual surfaces of spacelike curves in de Sitter 3-space, J. Nonlinear Sci. Appl., 9 (2016), 2563-2576
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T. Nagai , The Gauss map of a hyper surface in Euclidean sphere and the spherical Legendrian duality, Topology Appl., 159 (2012), 545-554
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S. Yilmaz, M. Turgut , A new version of Bishop frame and an application to spherical images, J. Math. Anal. Appl., 371 (2010), 764-776
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N. Yüksel , The ruled surfaces according to Bishop frame in Minkowski 3-space, Abstr. Appl. Anal., 2013 (2013), 1-5
]
A discretization iteration approach for solving a class of semivectorial bilevel programming problem
A discretization iteration approach for solving a class of semivectorial bilevel programming problem
en
en
The pessimistic optimal solution of the semivectorial bilevel programming problem with no upper level
variables in the lower level constraints is concerned. Based on the scalarization techniques and optimal
value transforming approach for the lower level problem, the semivectorial bilevel programming problem
is transformed into the corresponding infinite-dimensional optimization problem. Then, a discretization
iterative algorithm is proposed, and the convergence of the algorithm is also analyzed. The numerical
results show that the algorithm is feasible for the pessimistic optimal solution of the semivectorial bilevel
programming problem studied.
2888
2899
Yibing
Lv
School of Information and Mathematics
Yangtze University
P. R. China
lvyibing2001@gmail.com
Jiawei
Chen
School of Mathematics and Statistics
Southwest University
P. R. China
j.w.chen713@163.com
Semivectorial bilevel programming problem
optimal value function
discretization iteration
pessimistic solution.
Article.83.pdf
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[1]
Z. Ankhili, A. Mansouri , An exact penalty on bilevel programs with linear vector optimization lower level , European J. Oper. Res., 197 (2009), 36-41
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J. F. Bard, Practical Bilevel Optimization: Algorithm and Applications, Nonconvex Optim. Appl., Kluwer, Dordrecht (1998)
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B. Liu, Z. Wan, J. Chen, G. Wang, Optimality conditions for pessimistic semivectorial bilevel programming problems, J. Inequal. Appl., 2014 (2014), 1-26
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W. Wiesemann, A. Tsoukalas, P. M. Kleniati, B. Rustem, Pessimistic bilevel optimization, SIAM J. Optim., 23 (2013), 353-380
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Y. Zheng, Z. Wan , A solution method for semivectorial bilevel programming problem via penalty method, J. Appl. Math. Comput., 37 (2011), 207-219
]
Common fixed point results involving contractive condition of integral type in complex valued metric spaces
Common fixed point results involving contractive condition of integral type in complex valued metric spaces
en
en
By using the Closed Range Property of the involved pairs (in short CLR property), common fixed point
results for two pairs of weakly compatible mappings satisfying contractive condition of integral type in
complex valued metric spaces are established, which are new even in ordinary metric spaces. We furnish
suitable illustrative examples.
2900
2913
Mian Bahadur
Zada
Department of Mathematics
University of Malakand
Pakistan
mbz.math@gmail.com
Muhammad
Sarwar
Department of Mathematics
University of Malakand
Pakistan
sarwarswati@gmail.com
Nasir
Rahman
Department of mathematics and Statistics
Allam Iqbal open university
Pakistan
nasirzainy1@hotmail.com
Muhammad
Imdad
Department of Mathematics
Aligarh Muslim University
India
mhimdad@yahoo.co.in
Complex valued metric spaces
common fixed points
weakly compatible mappings
(E:A) property
(CLR) property.
Article.84.pdf
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[1]
M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188. , , , (), -
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M. Abbas, M. De la Sen, T. Nazir, Common fixed points of generalized cocyclic mappings in complex valued metric spaces, Discrete Dyn. Nat. Soc., 2015 (2015), 11 pages. , , , (), -
##[3]
J. Ahmad, N. Hussain, A. Azam, M. Arshad, Common fixed point results in complex valued metric space with applications to system of integral equations, J. Nonlinear Convex Anal., 16 (2015), 855-871., , , (), -
##[4]
[4] I. Altun, Common fixed point theorem for maps satisfying a general contractive condition of integral type, Acta Univ. Apulensis Math. Inform., 22 (2010), 195-206. , , , (), -
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I. Altun, D. Turkoglu, B. E. Rhoades, Fixed points of weakly compatible maps satisfying a general contractive condition of integral type, Fixed Point Theory Appl., 2007 (2007), 9 pages., , , (), -
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[6] A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 32 (2011), 243-253. , , , (), -
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S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math., 3 (1922), 133-181. , , , (), -
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A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531-536., , , (), -
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[10] S. Chandok, D. Kumar, Some common fixed point results for rational type contraction mappings in complex valued metric spaces, J. Oper., 2013 (2013), 6 pages. , , , (), -
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A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl., 329 (2007), 31-45. , , , (), -
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G. Jungck, Common fixed points for non-continuous non-self mappings on a non-numeric spaces, Far East J. Math. Sci., 4 (1996), 199-212. , , , (), -
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[14] J. Kumar, Common fixed point theorems of weakly compatible maps satisfying (E.A.) and (CLR) property, Int. J. Pure Appl. Math., 88 (2013), 363-376. , , , (), -
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M. A. Kutbi, J. Ahmad, A. Azam, A. S. Al Rawashdeh, Generalized common fixed point results via greatest lower bound property, J. Appl. Math., 2014 (2014), 11 pages. , , , (), -
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[16] M. A. Kutbi, M. Arshad, J. Ahmad, A. Azam, Generalized common fixed point results with applications, Abstr. Appl. Anal., 2014 (2014), 7 pages. , , , (), -
##[17]
Z. Liu, Y. Han, S. M. Kang, J. S. Ume, Common fixed point theorems for weakly compatible mappings satisfying contractive conditions of integral type, Fixed Point Theory Appl., 2014 (2014), 16 pages. , , , (), -
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[18] S. Manro, S. B. Jeong, S. M. Kang, Fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Anal., 7 (2013), 2811-2819. , , , (), -
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M. Mocanu, V. Popa, Some fixed point theorems for mappings satisfying implicit relations in symmetric spaces, Libertas Math., 28 (2008), 1-13., , , (), -
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[20] F. Rouzkard, M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl., 64 (2012), 1866-1874. , , , (), -
##[21]
M. Sarwar, M. Bahadur Zada, I. M. Erhan, Common fixed point theorems of integral type contraction on metric spaces and its applications to system of functional equations, Fixed Point Theory Appl., 2015 (2015), 15 pages. [, , , (), -
##[22]
22] W. Sintunavarat, P. Kumam, Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space, J. Appl. Math., 2011 (2011), 14 pages. , , , (), -
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W. Sintunavarat, P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequal. Appl., 2012 (2012), 12 pages. , , , (), -
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[24] R. K. Verma, H. K. Pathak, Common fixed point theorems using property (E.A) in complex-avlued metric spaces, Thai J. Math., 11 (2013), 347-355., , , (), -
]
Chen type inequality for warped product immersions in cosymplectic space forms
Chen type inequality for warped product immersions in cosymplectic space forms
en
en
Recently, Chen established a relation for the squared norm second fundamental form of warped product
immersion by using Codazzi equation. We establish a sharp inequality for a contact CR-warped product
submanifold in a cosymplectic space form by using the Gauss equation. The equality case is also discussed.
2914
2921
Siraj
Uddin
Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589 Jeddah, Saudi Arabia.
Lamia Saeed
Alqahtani
Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589 Jeddah, Saudi Arabia.
Warped product
contact CR-submanifold
inequality
cosymplectic manifold
\(N_T\)-minimal immersion.
Article.85.pdf
[
[1]
M. Atceken, Contact CR-warped product submanifolds in cosymplectic space forms, Collect. Math., 62 (2011), 17-26
##[2]
B.-Y. Chen, Another general inequality for CR-warped products in complex space forms, Hokkaido Math. J., 32 (2003), 415-444
##[3]
A. Mustafa, S. Uddin, B. R. Wong , Generalized inequalities on warped product submanifolds in nearly trans-Sasakian manifolds, J. Inequal. Appl., 2014 (2014), 1-15
##[4]
B. O'Neill , Semi-Riemannian geometry with applications to Relativity, Academic Press, New York (1983)
##[5]
S. Uddin, S. H. Kon, M. A. Khan, K. singh , Warped product semi-invariant submanifolds of nearly cosymplectic manifolds, Math. Probl. Eng., 2011 (2011), 1-12
]
Positive solutions for a class of fractional differential coupled system with integral boundary value conditions
Positive solutions for a class of fractional differential coupled system with integral boundary value conditions
en
en
This paper investigates the existence of positive solutions for the following high-order nonlinear fractional
differential boundary value problem (BVP, for short)
\[
\begin{cases}
D^\alpha_{0^+} u(t) + f(t,v(t))=0,\,\,\,\,\, t\in (0,1),\\
D^\alpha_{0^+} v(t) + g(t,u(t))=0,\,\,\,\,\, t\in (0,1),\\
u^{(j)}(0)=v^{(j)}(0)=0,\,\,\,\,\, 0\leq j\leq n-1, j\neq 1,\\
u'(1)=\lambda \int^1_0 u(t)d(t),\quad v'(1)=\lambda \int^1_0 v(t)d(t),
\end{cases}
\]
where \(n - 1 < \alpha\leq n; n \geq 3; 0 \leq\lambda < 2, D^\alpha_{0^+}\)
is the Caputo fractional derivative. By using the monotone
method, the theory of fixed point index on cone for differentiable operators and the properties of Green's
function, some new uniqueness and existence criteria for the considered fractional BVP are established. As
applications, some examples are worked out to demonstrate the main results.
2922
2942
Daliang
Zhao
Department of Mathematics
Shandong Normal University
P. R. China
likemoon07@sina.com
Yansheng
Liu
Department of Mathematics
Shandong Normal University
P. R. China
ysliu@sdnu.edu.cn
Fractional differential equations
differentiable operators
fixed point index theorems on cone
Article.86.pdf
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[1]
B. Ahmad, J. J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl., 58 (2009), 1838-1843
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B. Ahmad, J. J. Nieto, A. Alsaedi, M. El-Shahed , A study of nonlinear Langevin equation involving two fractional orders in different intervals, Nonlinear Anal. Real World Appl., 13 (2012), 599-606
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A. Cabada, G. Wang, Positive solutions of nonlinear fractional differential equations with integral boundary value conditions, J. Math. Anal. Appl., 389 (2012), 403-411
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C. S. Goodrich, Existence of a positive solution to a class of fractional differential equations, Appl. Math. Lett., 23 (2010), 1050-1055
##[5]
C. S. Goodrich, Existence of a positive solution to systems of differential equations of fractional order, Comput. Math. Appl., 62 (2011), 1251-1268
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##[7]
M. Jia, X. Liu, Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions, Appl. Math. Comput., 232 (2014), 313-323
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006)
##[9]
V. Lakshmikantham, A. S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal., 69 (2008), 2677-2682
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K. Q. Lan, W. Lin, Multiple positive solutions of systems of Hammerstein integral equations with applications to fractional differential equations, J. Lond. Math. Soc., 83 (2011), 449-469
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]
The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems
The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems
en
en
In this paper we study a class of operator equations \(A(x; x) + B(x; x) = x\) in ordered Banach spaces,
where A;B are two mixed monotone operators. Various theorems are established to guarantee the existence
of a unique solution to the problem. In addition, associated iterative schemes have been established for
finding the approximate solution converging to the fixed point of the problem. We also study the solution
of the nonlinear eigenvalue equation \(A(x; x) + B(x; x) = \lambda x\) and discuss its dependency to the parameter.
Our results extend and improve many known results in this field of study. We have also successfully
demonstrated the application of our results to the study of nonlinear fractional differential equations with
two-point boundary conditions.
2943
2958
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University
P. R. China
Australia
mathlls@163.com
Xinqiu
Zhang
School of Mathematical Sciences
Qufu Normal University
P. R. China
1257368359@qq.com
Juan
Jiang
School of Mathematical Sciences
Qufu Normal University
P. R. China
872383169@qq.com
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University
Australia
yhwu@maths.curtin.edu.au
Mixed monotone operator
hypo-homogeneous mixed monotone operator
existence and uniqueness
fractional differential equation.
Article.87.pdf
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]
Auxiliary principle and iterative algorithms for generalized mixed nonlinear variational-like inequalities
Auxiliary principle and iterative algorithms for generalized mixed nonlinear variational-like inequalities
en
en
The aim of this paper is to study the solvability of a class of generalized mixed nonlinear variational-
like inequalities in Hilbert spaces. Using the auxiliary principle technique, the Banach fixed-point theorem
and an inequality due to Chang and Xiang, we construct two iterative algorithms for finding approximate
solutions of the generalized mixed nonlinear variational-like inequality. Under some conditions we prove
the existence and uniqueness of solution for the generalized mixed nonlinear variational-like inequality and
establish the strong convergence of approximate solutions to the exact solution of the generalized mixed
nonlinear variational-like inequality. Our results extend, improve and unify some known results in the
literature.
2959
2970
Zeqing
Liu
Department of Mathematics
Liaoning Normal University Dalian
P. R. China
zeqingliu@dl.cn
Pingping
Zheng
Department of Mathematics
Liaoning Normal University Dalian
P. R. China
pingpingzheng@live.cn
Jeong Sheok
Ume
Department of Mathematics
Changwon National University
Korea
jsume@changwon.ac.kr
Shin Min
Kang
Department of Mathematics and the Research Institute of Natural Science
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Generalized mixed nonlinear variational-like inequality
Banach fixed-point theorem
auxiliary principle technique
iterative algorithm with errors.
Article.88.pdf
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]
Weak solutions to boundary value problems for fractional differential equations via variational methods
Weak solutions to boundary value problems for fractional differential equations via variational methods
en
en
Using variational methods, we investigate the solutions to the boundary value problems for fractional
order differential equations. First, we consider the eigenvalue problem associated with it. Then, we obtain
the existence of at least two weak solutions for every real number via Brezis and Nirenberg's Linking
Theorem. Furthermore, for every positive integer k, the existence criteria of k pairs of weak solutions are
established by using Clark Theorem. At last, some examples are also given to illustrate the results.
2971
2981
Peiluan
Li
School of Mathematics and Statistics
Henan University of Science and Technology
P. R. China
lpllpl_lpl@163.com
Changjin
Xu
Guizhou Key Laboratory of Economics System Simulation
Guizhou College of Finance and Economics
P. R. China
xcj403@126.com
Hui
Wang
College of Information Engineering
Henan University of Science and Technology
P. R. China
wh@haust.edu.cn
Fractional differential equations
critical points
variational method
eigenvalue problem.
Article.89.pdf
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##[3]
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N. Nyamoradi, R. Rodriguez-Lopez, On boundary Value Problems for Impulsive Fractional Differential equations, Appl. Math. Comput., 271 (2015), 874-892
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]
Adomian decomposition method for n-dimensional diffusion model in fractal heat transfer
Adomian decomposition method for n-dimensional diffusion model in fractal heat transfer
en
en
A nondifferentiable analytical solution of the \(n\)-dimensional diffusion equation in fractal heat transfer is
investigated using the local fractional Adomian decomposition method.
2982
2985
Badr S.
Alkahtani
Department of Mathematics, College of Sciences
King Saud University
Saudi Arabia
Pranay
Goswami
School of Liberal Studies
Ambedkar University Delhi
India
pranaygoswami83@gmail.com
Obaid J.
Algahtani
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
obalgahtani@ksu.edu.sa
Adomian decomposition method
\(n\)-dimensional diffusion equation
fractal heat transfer
local fractional derivative.
Article.90.pdf
[
[1]
B. S. Alkahtani, V. Gulati, P. Goswami, On the Solution of Generalized Space Time Fractional Telegraph Equation, Math. Probl. Eng., 2015 (2015), 1-7
##[2]
Z. P. Fan, H. K. Jassim, R. K. Raina, X.-J. Yang, Adomian Decomposition Method for Three Dimensional Diffusion Model in Fractal Heat Transfer Involving Local Fractional Derivatives, Thermal Sci., 19 (2015), 137-141
##[3]
P. Goswami, R. T. Alqahtani, On the Solution of Local Fractional Differential Equations Using Local Fractional Laplace Variational Iteration Method, Math. Probl. Eng., 2016 (2016), 1-6
##[4]
X.-J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong (2011)
##[5]
X.-J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York (2012)
##[6]
X.-J. Yang, D. Baleanu, P. Lazarevic Mihailo, S. Cajic Milan, Fractal Boundary Value Problems for Integral and Differential Equations with Local Fractional Operators, Thermal Sci., 19 (2015), 959-966
##[7]
X.-J. Yang, D. Baleanu, H. M. Srivastava, Local Fractional Integral Transforms and Their Applications, Academic Press, Amesterdam (2016)
##[8]
X.-J. Yang, D. Baleanu, W.-P. Zhong, Approximate solutions for diffusion equations on Cantor space-time, Proc. Romanian Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci., 14 (2013), 127-133
]
Heat flux performance in a porous medium embedded Maxwell fluid flow over a vertically stretched plate due to heat absorption
Heat flux performance in a porous medium embedded Maxwell fluid flow over a vertically stretched plate due to heat absorption
en
en
Heat absorption and thermal radiation effects in a non-Newtonian
fluid on a vertical stretching sheet with
suspended particles are considered. The nonlinear partial differential equations are reduced to nonlinear
ordinary differential equations via similarity approach. The equations are further solved using shooting-
RK4 method and validated with homotopy-Padé solutions. Comparison between previous and present
results revealed agreement up to five significant figures. The in
uence of various parameters on the
flow
velocity, temperature and concentration are examined. The profiles of reduced skin friction coefficient,
Nusselt number and Sherwood number against selected parameters are sketched and discussed. Streamlines
of the
flow for different Maxwell parameters are visualized too. It is proclaimed that the heat
flux of the
flow
is uplifted as value of either heat absorption or thermal radiation is multiplied.
2986
3001
N. F. M.
Noor
Institute of Mathematical Sciences, Faculty of Science
University of Malaya
Malaysia
drfadiya@um.edu.my
R. U.
Haq
Department of Mathematics
Capital University of Science and Technology
Pakistan
S.
Abbasbandy
Department of Mathematics
Imam Khomeini International University
Iran
I.
Hashim
School of Mathematical Sciences
Research Institute, Center for Modeling & Computer Simulation (RI/CM&CS)
Universiti Kebangsaan Malaysia
King Fahd University of Petroleum & Minerals
Malaysia
Saudi Arabia
Maxwell
thermophoresis
homotopy-Padé
shooting
heat absorption
thermal radiation.
Article.91.pdf
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[1]
M. S. Abel, J. V. Tawade, M. M. Nandeppanavar, MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet, Meccanica, 47 (2012), 385-393
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C. Fetecau, C. Fetecau, A new exact solution for the flow of a Maxwell fluid past an infinite plate, Int. J. Non- Linear Mech., 38 (2003), 423-427
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F. Guerrero, F. J. Santonja, R. J. Villanueva, Solving a model for the evolution of smoking habit in Spain with homotopy analysis method, Nonlinear Anal. Real World Appl., 14 (2013), 549-558
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Approximation of solutions of quasi-variational inclusions and fixed points of nonexpansive mappings
Approximation of solutions of quasi-variational inclusions and fixed points of nonexpansive mappings
en
en
The purpose of this article is to study common solution problems of quasi-variational inclusion problems
and nonlinear operator equations involving nonexpansive mappings. Strong convergence theorems are obtained without any compactness assumptions imposed on the operators and the spaces.
3002
3009
Dongfeng
Li
School of Information Engineering
North China University of Water Resources and Electric Power
China
sylidf@yeah.net
Juan
Zhao
School of Mathematics and Information Sciences
North China University of Water Resources and Electric Power University
China
zhaojuanyu@126.com
Hilbert space
convergent theorem
fixed point
contractive mapping
monotone operator.
Article.92.pdf
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Omega open sets in generalized topological spaces
Omega open sets in generalized topological spaces
en
en
We extend the notion of omega open set in ordinary topological spaces to generalized topological spaces.
We obtain several characterizations of omega open sets in generalized topological spaces and prove that they
form a generalized topology. Using omega open sets we introduce characterizations of Lindelöf, compact, and
countably compact concepts generalized topological spaces. Also, we generalize the concepts of continuity
in generalized topological spaces via omega open sets.
3010
3017
Samer Al
Ghour
Department of Mathematics and Statistics
Jordan University of Science and Technology
Jordan
algore@just.edu.jo
Wafa
Zareer
Department of Mathematics and Statistics
Jordan University of Science and Technology
Jordan
Generalized topology
\(\omega\)-open sets
continuous functions
Lindelöf
compact
countably compact.
Article.93.pdf
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K. Al-Zoubi, On generalized \(\omega\)-closed sets, Int. J. Math. Math. Sci., 13 (2005), 2011-2021
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]
Non-Nehari manifold method for a semilinear Schrödinger equation with critical Sobolev exponent
Non-Nehari manifold method for a semilinear Schrödinger equation with critical Sobolev exponent
en
en
We consider the semilinear Schrödinger equation
\[
\begin{cases}
-\Delta u + V (x)u = K(x)|u|^{2^*-2}u + f(x; u);\, x\in R^N,\\
u \in H^1(R^N),
\end{cases}
\]
where \(N \geq 4, 2^* := 2N/(N - 2)\) is the critical Sobolev exponent, V;K; f is 1-periodic in \(x_j\) for \(j = 1; ... ;N,
f(x; u)\) is subcritical growth. We develop a direct approach to find ground state solutions of Nehari-Pankov
type for the above problem. The main idea is to find a minimizing Cerami sequence for the energy functional
outside the Nehari-Pankov manifold by using the diagonal method.
3018
3030
Huxiao
Luo
School of Mathematics and Statistics
Central South University
P. R. China
wshrm7@126.com
Xianhua
Tang
School of Mathematics and Statistics
Central South University
P. R. China
tangxh@mail.csu.edu.cn
Jianhua
Chen
School of Mathematics and Statistics
Central South University
P. R. China
Jian
Zhang
School of Mathematics and Statistics
Hunan University of Commerce
P. R. China
Schrödinger equation
ground state solutions of Nehari-Pankov type
critical Sobolev exponent
non-Nehari-manifold method.
Article.94.pdf
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X. Lin, X. H. Tang, Semiclassical solutions of perturbed p-Laplacian equations with critical nonlinearity, J. Math. Anal. Appl., 413 (2014), 438-449
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X. Lin, X. H. Tang, Nehari-type ground state solutions for superlinear asymptotically periodic Schrodinger equations, Abstr. Appl. Anal., 2014 (2014), 1-7
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X. Lin, X. H. Tang, An asymptotically periodic and asymptotically linear Schrodinger equation with indefinite linear part, Comput. Math. Appl., 70 (2015), 726-736
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S. Liu , On superlinear Schrodinger equations with periodic potential , Calc. Var. Partial Differential Equation, 45 (2012), 1-9
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A. Pankov, Periodic nonlinear Schrodinger equations, Milan. J. Math., 73 (2005), 259-287
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X. H. Tang, Infinitely many solutions for semilinear Schrodinger equations with sign-changing potential and nonlinearity, J. Math. Anal. Appl., 401 (2013), 407-415
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X. H. Tang , New conditions on nonlinearity for a periodic Schrodinger equation having zero as spectrum, J. Math. Anal. Appl., 413 (2014), 1-392
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X. H. Tang, New super-quadratic conditions on ground state solutions for superlinear Schrodinger equation, Adv. Nonlinear Stud., 14 (2014), 361-373
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X. H. Tang , Non-Nehari manifold method for asymptotically periodic Schrodinger equations , Sci. China. Math., 58 (2015), 715-728
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X. H. Tang, Non-Nehari manifold method for asymptotically linear Schrodinger equation, J. Aust. Math. Soc., 98 (2015), 104-116
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X. H. Tang, S. T. Chen, Weak potential conditions for Schrodinger equations with critical nonlinearities , J. Aust. Math. Soc., 100 (2015), 1-1
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M. Yang, Ground state solutions for a periodic periodic Schrodinger equation with superlinear nonlinearities, Nonlinear. Anal., 72 (2010), 2620-2627
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J. Zhang, X. H. Tang, W. Zhang, Semiclassical solutions for a class of Schrodinger system with magnetic potentials, J. Math. Anal. Appl., 414 (2014), 357-371
]
Coincidence type alternatives for \(\Phi\)--essential maps
Coincidence type alternatives for \(\Phi\)--essential maps
en
en
In this paper we present some criteria for \(\Phi\)-essential maps and as a consequence these generate a number
of new Leray-Schauder type alternatives.
3031
3035
Donal
ORegan
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
Ireland
donal.oregan@nuigalway.ie
Essential maps
coincidence points
Leray-Schauder alternatives.
Article.95.pdf
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[1]
M. Furi, M. Martelli, A. Vignoli , On the solvability of nonlinear operator equations in normed spaces, Ann. Math. Pura Appl., 124 (1980), 321-343
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G. Gabor, L. Gorniewicz, M. Slosarski, Generalized topological essentiality and coincidence points of multivalued maps, Set-Valued Var. Anal., 17 (2009), 1-19
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##[5]
D. O'Regan, Coincidence points for multivalued maps based on \(\Phi\)-epi and \(\Phi\)-essential maps, Dynam. Systems Appl., 24 (2015), 143-154
]
Some coincidence point theorems for g-monotone increasing multi-valued mappings in cone metric spaces over Banach algebras
Some coincidence point theorems for g-monotone increasing multi-valued mappings in cone metric spaces over Banach algebras
en
en
In this paper, in partially ordered cone metric spaces over Banach algebras, we introduce the concept
of g-monotone mappings and prove some coincidence point theorems for multi-valued and single-valued
g-monotone increasing mappings satisfying certain metric inequalities which are established by an altering
distance function. The presented results extend and improve some recent results. An illustrative example
is given to support our results.
3036
3047
Jiandong
Yin
Department of Mathematics
Nanchang University
P. R. China
yjdaxf@163.com
Qianqian
Leng
Department of Mathematics
Nanchang University
P. R. China
13517914026@163.com
Haoran
Zhu
Department of Mathematics
Nanchang University
P. R. China
haoranzhu@163.com
Sangsang
Li
Department of Mathematics
Nanchang University
P. R. China
lss88888888@sina.cn
Multi-valued mappings
g-increasing mapping
altering functions.
Article.96.pdf
[
[1]
B. S. Choudhury, A common unique fixed point result in metric spaces involving generalised altering distances, Math. Commun., 10 (2005), 105-110
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B. S. Choudhury, N. Metiya, Multi-valued and single-valued fixed point results in partially ordered metric spaces, Arab J. Math. Sci., 17 (2011), 131-135
##[3]
L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
##[4]
M. A. Khamsi, A. R. Khan, Inequalities in metric spaces with applications , Nonlinear Anal., 74 (2011), 4036-4045
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A. R. Khan, A. A. Domolo, N. Hussain, Coincidence of Lischitz-type hybird maps and invariant approximation, Numer. Funct. Anal. Optim., 28 (2007), 1165-1177
##[6]
H. Liu, S. Y. Xu , Fixed point theorem of quasi-contractions on cone metric spaces with Banach algebras, Abstr. Appl. Anal., 2013 (2013), 1-5
##[7]
H. Liu, S. Y. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl., 2013 (2013), 1-10
##[8]
Sh. Rezapour, R. Hamlbarani, Some notes on the paper Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 345 (2008), 719-724
##[9]
S. Y. Xu, S. Radenovic, Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality, Fixed Point Theory Appl., 2014 (2014), 1-12
]
Nonparametric robust function estimation for integrated diffusion processes
Nonparametric robust function estimation for integrated diffusion processes
en
en
This paper considers local M-estimation of the unknown drift and diffusion functions of integrated
diffusion processes. We show that under appropriate conditions, the proposed estimators for drift and
diffusion functions in the integrated process are consistent, and the conditions that ensure the asymptotic
normality of these local M-estimators are also stated. The simulation studies show that the proposed
estimators perform better than the kernel estimator in robustness.
3048
3065
Yunyan
Wang
School of Science
Jiangxi University of Science and Technology
P. R. China
yywang@zju.edu.cn
Mingtian
Tang
School of Science
Jiangxi University of Science and Technology
P. R. China
mttang_csu@yahoo.com
Integrated diffusion process
local linear estimator
M-estimation
robust estimation.
Article.97.pdf
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[1]
L. Arnold, Stochastic differential equations: Theory and Application, Wiley, New York (1974)
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F. Bandi, P. Phillips, Fully nonparametric estimation of scalar diffusion models, Econometrica, 71 (2003), 241-283
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S. Ditlevsen, M. Srensen, Inference for observations of integrated diffusion processes, Scand. J. Statist., 31 (2004), 417-429
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On n-collinear elements and Riesz theorem
On n-collinear elements and Riesz theorem
en
en
In this paper, we prove that the n-collinear elements \(x_1; x_2; : ... ; x_n; u\) satisfy some special relations in an
n-normed space X. Further, we prove that \(u =\frac{ x_1+...+x_n}{n}\) is the only unique element in the n-normed space
X such that \(x_1; x_2; ... ; x_n; u\) are n-collinear elements in X satisfying some specified inequalities. Moreover,
we prove that the Riesz theorem holds when X is a linear n-normed space.
3066
3073
Wasfi
Shatanawi
Department of Mathematics
Hashemite University
Jordan
swasfi@hu.edu.jo
Mihai
Postolache
Department of Mathematics and Informatics
University Politehnica of Bucharest
Romania
mihai@mathem.pub.ro
n-normed space
invex set
linearly dependent
collinear elements.
Article.98.pdf
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Dynamics of a predator-prey system with stage structure and two delays
Dynamics of a predator-prey system with stage structure and two delays
en
en
A Holling type III predator-prey system with stage structure for the predator and two delays is inves-
tigated. At first, we study the stability and the existence of periodic solutions via Hopf bifurcation with
respect to both delays at the positive equilibrium by analyzing the distribution of the roots of the associated
characteristic equation. Then, explicit formulas that can determine the direction of the Hopf bifurcation
and the stability of the periodic solutions bifurcating from the Hopf bifurcation are established by using the
normal form method and center manifold argument. Finally, some numerical simulations are carried out to
support the main theoretical results.
3074
3089
Juan
Liu
Department of Mathematics and Physics
Bengbu University
P. R. China
my7216@163.com
Zizhen
Zhang
School of Management Science and Engineering
Anhui University of Finance and Economics
P. R. China
zzzhaida@163.com
Delays
Hopf bifurcation
periodic solutions
predator-prey system
stability.
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R. Xu, Global dynamics of a predator-prey model with time delay and stage structure for the prey, Nonlinear Anal. Real World Appl., 12 (2011), 2151-2162
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]
On approximation properties of certain multidimensional nonlinear integrals
On approximation properties of certain multidimensional nonlinear integrals
en
en
We prove theorems on convergence of multidimensional nonlinear integrals in Lebesgue points of generated function, and show that the main results are applicable to a wide class of exponentially nonlinear
integral operators, which may be constructed by using well known positive kernels in approximation theory.
3090
3097
Sevgi Esen
Almali
Faculty of Sciences and Art, Depatment of Mathematics
Kirikkale University
Turkey
sevgi_esen@hotmail.com
Akif D.
Gadjiev
National Academy of Sciences of Azerbaijan
Azerbaijan
akif_gadjiev@mail.us
Nonlinear integral operators
positive kernels
Lebesgue points
approximation
exponentially nonlinear integrals.
Article.100.pdf
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C. Bardaro, G. Vinti, H. Karsli , Nonlinear integral operators with homogeneous kernels: pointwise approximation theorems , Appl. Anal., 90 (2011), 463-474
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Differential equations associated with lambda-Changhee polynomials
Differential equations associated with lambda-Changhee polynomials
en
en
In this paper, we study linear differential equations arising from \(\lambda\)-Changhee polynomials (or called
degenerate Changhee polynomials) and give some explicit and new identities for the \(\lambda\)-Changhee polynomials
associated with linear differential equations.
3098
3111
Taekyun
Kim
Department of Mathematics
Kwangwoon University
Republic of Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Jong-Jin
Seo
Department of Applied Mathematics
Pukyong National University
Republic of Korea
seo2011@pknu.ac.kr
Hyuck-In
Kwon
Department of Mathematics
Kwangwoon University
Republic of Korea
sura@kw.ac.kr
\(\lambda\)-Changhee polynomials
differential equations.
Article.101.pdf
[
[1]
A. Bayad, T. Kim, Higher recurrences for Apostol-Bernoulli-Euler numbers , Russ. J. Math. Phys., 19 (2012), 1-10
##[2]
D. Ding, J. Yang, Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math., (Kyungshang), 20 (2010), 7-21
##[3]
L.-C. Jang, C. S. Ryoo, J. J. Seo, H. I. Kwon, Some properties of the twisted Changhee polynomials and their zeros, Appl. Math. Comput., 274 (2016), 169-177
##[4]
T. Kim, Non-Archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys., 10 (2003), 91-98
##[5]
T. Kim, D. V. Dolgy, D. S. Kim, J. J. Seo, Di erential equations for Changhee polynomials and their applications, J. Nonlinear Sci. Appl., 9 (2016), 2857-2864
##[6]
D. S. Kim, T. Kim, A note on Boole polynomials, Integral Transforms Spec. Funct., 25 (2014), 627-633
##[7]
D. S. Kim, T. Kim, Some identities for Bernoulli numbers of the second kind arising from a nonlinear differential equation, Bull. Korean. Math. Soc., 52 (2015), 2001-2010
##[8]
D. S. Kim, T. Kim , Some identities of Korobov-type polynomials associated with p-adic integrals on Zp, Adv. Difference Equ., 2015 (2015), 1-13
##[9]
T. Kim, D. S. Kim, A note on non-linear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88-92
##[10]
D. S. Kim, T. Kim, T. Komatsu, S.-H. Lee, Barnes-type Daehee of the first kind and poly-Cauchy of the first kind mixed-type polynomials, Adv. Difference Equ., 2014 (2014), 1-22
##[11]
D. S. Kim, T. Kim, J. J. Seo, A note on q-analogue of Boole polynomials, Appl. Math. Inf. Sci., 9 (2015), 3135-3158
##[12]
T. Kim, T. Mansour, S. H. Rim, J. J. Seo, A note on q-Changhee polynomials and numbers, Adv. Stud. Theor. Phys., 8 (2014), 35-41
##[13]
H. I. Kwon, T. Kim, J. J. Seo , A note on degenerate Changhee numbers and polynomials, Proc. Jangjeon Math. Soc., 18 (2015), 295-305
##[14]
D. Lim, F. Qi, On the appell type{changhee polynomials, J. Nonlinear Sci. Appl., 9 (2016), 1872-1876
##[15]
J.-W. Park, On the twisted q-Changhee polynomials of higher order, J. Comput. Anal. Appl., 20 (2016), 424-431
##[16]
S.-H. Rim, J.-W. Park, S.-S. Pyo, J. Kwon, The n-th twisted Changhee polynomials and numbers, Bull. Korean. Math. Soc., 52 (2015), 741-749
##[17]
J. J. Seo, T. Kim, p-adic invariant integral on Zp associated with the Changhee's q-bernoulli polynomials, Int. J. Math. Anal. (Ruse), 7 (2013), 2117-2128
##[18]
G. Y. Sohn, J. K. Kwon, A note on twisted Changhee polynomials and numbers with weight, Appl. Math. Sci., 9 (2015), 1517-1525
##[19]
N. L. Wang, L. Hailong, Some identities on the higher-order Daehee and Changhee numbers, Pure Appl. Math. J., 4 (2015), 33-37
]
Properties and integral inequalities of Hadamard- Simpson type for the generalized \((s,m)\)-preinvex functions
Properties and integral inequalities of Hadamard- Simpson type for the generalized \((s,m)\)-preinvex functions
en
en
The authors introduce the concepts of m-invex set, generalized \((s,m)\)-preinvex function, and explicitly
\((s,m)\)-preinvex function, provide some properties for the newly introduced functions, and establish new
Hadamard-Simpson type integral inequalities for a function of which the power of the absolute of the first
derivative is generalized \((s,m)\)-preinvex function. By taking different values of the parameters, Hadamardtype
and Simpson-type integral inequalities can be deduced. Furthermore, inequalities obtained in special
case present a refinement and improvement of previously known results.
3112
3126
Ting-Song
Du
College of Science
Hubei Province Key Laboratory of System Science in Metallurgical Process
China Three Gorges University
Wuhan University of Science and Technology
P. R. China
P. R. China
tingsongdu@ctgu.edu.cn
Jia-Gen
Liao
College of Science
China Three Gorges University
P. R. China
JiagenLiao@163.com
Yu-Jiao
Li
College of Science
China Three Gorges University
P. R. China
yujiaolictgu@163.com
Integral inequalities of Hadamard-Simpson type
Hölder's inequality
\((s،m)\)-preinvex function.
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A. Barani, A. G. Ghazanfari, S. S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex , J. Inequal. Appl., 2012 (2012), 1-9
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F. Chen, S. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9 (2016), 705-716
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M. A. Latif, M. Shoaib, Hermite-Hadamard type integral inequalities for differentiable m-preinvex and (\(\alpha,m\))- preinvex functions , J. Egyptian Math. Soc., 23 (2015), 236-241
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Y. J. Li, T. S. Du, Some Simpson type integral inequalities for functions whose third derivatives are (\(\alpha,m\))-GA- convex functions, J. Egyptian Math. Soc., 24 (2016), 175-180
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M. Mat loka, Inequalities for h-preinvex functions, Appl. Math. Comput., 234 (2014), 52-57
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J. Park , Simpson-like and Hermite-Hadamard-like type integral inequalities for twice differentiable preinvex functions, Inter. J. Pure. Appl. Math., 79 (2012), 623-640
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S. Qaisar, C. J. He, S. Hussain, A generalizations of Simpson's type inequality for di erentiable functions using (\(\alpha,m\))-convex functions and applications, J. Inequal. Appl., 2013 (2013), 1-13
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M. H. Qu, W. J. Liu, J. Park, Some new Hermite-Hadamard-type inequalities for geometric-arithmetically s- convex functions, WSEAS Trans. Math., 13 (2014), 452-461
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S. H. Wang, X. M. Liu, Hermite-Hadamard type inequalities for operator s-preinvex functions , J. Nonlinear Sci. Appl., 8 (2015), 1070-1081
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Y. Wang, B. Y. Xi, F. Qi, Hermite-Hadamard type integral inequalities when the power of the absolute value of the first derivative of the integrand is preinvex, Matematiche (Catania), 69 (2014), 89-96
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]
1-Lightlike surfaces in semi-Euclidean 4-space with index two
1-Lightlike surfaces in semi-Euclidean 4-space with index two
en
en
By establishing some differential geometry theory on the 1-lightlike surfaces, we show several geometric
properties of the 1-lightlike surfaces which are completely different from non-lightlike surfaces. Based on
these theories, we consider the singularities of the 1-lightlike surfaces in semi- Euclidean 4-space with index
two as an application of the theory of Legendrian singularities. We characterize the singularities of the
1-lightlike focal hypersurfaces and describe the contacts between the 1-lightlike surface and the anti de
Sitter 3-sphere at singular points by employing Montaldi's theory. In addition, we also discuss the detailed
differential geometric properties of the 1-lightlike focal hypersurfaces in semi-Euclidean 4-space with index
2. Finally, an example will be proposed to explain our findings.
3127
3146
Qiuyan
Wang
School of Mathematical Sciences
Harbin Normal University
P. R. China
qywang0112@163.com
Zhigang
Wang
School of Mathematical Sciences
Harbin Normal University
P. R. China
wangzg2003205@163.com
Hermite-Hadamard's inequality
Hermite-Hadamard's inequality
anti de Sitter space
Legendrian singularity.
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Semi-metric spaces and fixed points of \(\alpha-\varphi\)-contractive maps
Semi-metric spaces and fixed points of \(\alpha-\varphi\)-contractive maps
en
en
A negative answer to an open problem is provided. Fixed point results for \(\alpha-\varphi\)-contractive mappings
in semi-metric spaces are proved. To show the generality of our results, examples are given. Finally, an
application of our result to probabilistic spaces is derived.
3147
3156
Naseer
Shahzad
Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
nshahzad@kau.edu.sa
Mohammed Ali
Alghamdi
Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Proff-malghamdi@hotmail.com
Sarah
Alshehri
Department of Mathematics
King Abdulaziz University, Science Faculty for Girls
Saudi Arabia
Ivan
Arandelovic
Faculty of Mechanical Engineering
University of Belgrade
Serbia
iarandjelovic@mas.bg.ac.rs
Semi-metric space
\(\alpha-\varphi\)-contractive mapping
fixed point
probabilistic space.
Article.104.pdf
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On convergence of random iterative schemes with errors for strongly pseudo-contractive Lipschitzian maps in real Banach spaces
On convergence of random iterative schemes with errors for strongly pseudo-contractive Lipschitzian maps in real Banach spaces
en
en
In this work, strong convergence and stability results of a three step random iterative scheme with errors
for strongly pseudo-contractive Lipschitzian maps are established in real Banach spaces. Analytic proofs
are supported by providing numerical examples. Applications of random iterative schemes with errors
to find solution of nonlinear random equation are also given. Our results improve and establish random
generalization of results obtained by Xu and Xie [Y. Xu, F. Xie, Rostock. Math. Kolloq., 58 (2004), 93-100],
Gu and Lu [F. Gu, J. Lu, Math. Commun., 9 (2004), 149-159], Liu et al. [Z. Liu, L. Zhang, S. M. Kang,
Int. J. Math. Math. Sci., 31 (2002), 611-617] and many others.
3157
3168
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Satish
Narwal
Department of Mathematics
S. J. K. College Kalanaur
India
narwalmaths@gmail.com
Renu
Chugh
Department of Mathematics
M. D. University
India
chughrenu@yahoo.com
Vivek
Kumar
Department of Mathematics
K. L. P. College
India
ratheevivek15@yahoo.com
Random Iterative schemes
stability
strongly pseudo-contractive maps.
Article.105.pdf
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]
Topological properties of L-partial pseudo-quasi- metric spaces
Topological properties of L-partial pseudo-quasi- metric spaces
en
en
As an application of partial metrics and fuzzy set theory, the concept of L-partial pseudo-quasi-metric
spaces is introduced and its topological properties are investigated. It is shown that L-partial pseudo-quasi-
metrics are reasonable generalizations of partial pseudo-quasi-metrics and pointwise metrics in the sense of
Shi. Also, it is proved that an L-partial pseudo-quasi-metric space can be endowed with an L-cotopology
and a pointwise quasi-uniformity. Moreover, an L-partial pseudo-quasi-metric and its induced pointwise
quasi-uniformity induce the same L-cotopology.
3169
3178
Zhen-Yu
Xiu
College of Applied Mathematics
Chengdu University of Information Technology
China
xiuzhenyu112@sohu.com
Bin
Pang
Shenzhen Graduate School
Harbin Institute of Technology
China
pangbin1205@163.com
Partial metric
L-partial metric
L-cotopology
pointwise metric.
Article.106.pdf
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]
The Form of the Solutions of Nonlinear Difference Equations Systems
The Form of the Solutions of Nonlinear Difference Equations Systems
en
en
In this paper, we deal with the form of the solutions of the following nonlinear difference equations
systems
\[x_{n+1} =\frac{x_{n-7}}{1 + x_{n-7}y_{n-3}}
; y_{n+1} =\frac{y_{n-7}}{\pm 1 \pm x_{n-3}y_{n-7}};\]
where the initial conditions \(x_{-7}; x_{-6}; x_{-5}; x_{-4}; x_{-3}; x_{-2}; x_{-1}; x_0; y_{-7}; y_{-6}; y_{-5}; y_{-4}; y_{-3}; y_{-2}; y_{-1}; y_0\)
are real numbers.
3179
3196
E. M.
Elsayed
Mathematics Department, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
Mansoura University
Saudi Arabia
Egypt
emmelsayed@yahoo.com
A.
Alghamdi
Mathematics Department, Faculty of Science
Mathematics Department
King Abdulaziz University
University College of Umluj, Tabuk University
Saudi Arabia
Saudi Arabia
asm-alghamdi@hotmail.com
Difference equations
system of difference equations
solution of difference equation.
Article.107.pdf
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E. M. Elsayed, A. M. Ahmed, Dynamics of a three-dimensional systems of rational difference equations , Math. Methods Appl. Sci., 39 (2016), 1026-1038
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Tripled fixed point theorems for contractions in partially ordered \(L\)-fuzzy normed spaces
Tripled fixed point theorems for contractions in partially ordered \(L\)-fuzzy normed spaces
en
en
Recently, Kumam, et al. in [P. Kumam, J. Martinez-Moreno, A. Roldán, C. Roldán, J. Inequal. Appl.,
2014 (2014), 7 pages] proved some tripled fixed point theorems in fuzzy normed spaces. In this paper, we
give a new version of the result of Kumam, et al. by removing some restrictions. In our result, the t-norms
are not required to be the minimum ones.
3197
3202
Juan
Martínez-Moreno
Departamento de Matemáticas
Universidad de Jaén
Spain
jmmoreno@ujaen.es
Poom
Kumam
Department of Mathematics & Theoretical and Computational Science Center (TaCS), Science Laboratory Building
Department of Medical Research
Faculty of Science King Mongkuts University of Technology Thonburi (KMUTT)
China Medical University Hospital, China Medical University
Thailand
Taiwan
poom.kum@kmutt.ac.th
Fuzzy normed space
tripled fixed point
fixed point
t-norm.
Article.108.pdf
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[1]
M. Abbas, B. Ali, W. Sintunaravat, P. Kumam , Tripled fixed point and tripled coincidence point theorems in intuitionistic fuzzy normed spaces , Fixed Point Theory Appl., 2012 (2012), 1-16
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M. Abbas, H. Aydi, E. Karapinar , Tripled fixed points of multivalued nonlinear contraction mappings in partially ordered metric spaces , Abstr. Appl. Anal., 2011 (2011), 1-12
##[3]
H. Aydi, E. Karapinar , New Meir-Keeler type tripled fixed-point theorems on ordered partial metric spaces , Math. Probl. Eng., 2012 (2012), 1-17
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P. Kumam, J. Martinez-Moreno, A. Roldan, C. Roldan , Berinde-Borcut tripled fixed point theorem in partially ordered (intuitionistic) fuzzy normed spaces , J. Inequal. Appl., 2014 (2014), 1-7
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]
Stability of Efficient Solutions for Semi-infinite Vector Optimization Problems
Stability of Efficient Solutions for Semi-infinite Vector Optimization Problems
en
en
This paper is devoted to the study of the stability of efficient solutions for semi-infinite vector optimization
problems (SIO). We first obtain the closedness, Berge-lower semicontinuity and Painlevé-Kuratowski
convergence of constraint set mapping. Then, under the assumption of continuous convergence of the objective
function, we establish some sufficient conditions of the upper Painlevé-Kuratowski stability of efficient
solution mappings to the (SIO). Some examples are also given to illustrate the results.
3203
3211
Zai-Yun
Peng
College of Mathematices and Statistices
Chongqing JiaoTong University
P. R. China
pengzaiyun@126.com
Jian-Ting
Zhou
College of Civil Engineering
Chongqing JiaoTong University
P. R. China
jt-zhou@163.com
Upper Painlevé-Kuratowski stability
semi-infinite vector optimization
perturbation
efficient solution
continuous convergence.
Article.109.pdf
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]
Multiplicity solutions for discrete fourth-order boundary value problem with multiple parameters
Multiplicity solutions for discrete fourth-order boundary value problem with multiple parameters
en
en
In this paper, we consider the existence of three solutions and infinitely many solutions for discrete
fourth-order boundary value problems with multiple parameters under the different suitable hypotheses,
respectively. The approach we use is the critical point theory.
3212
3225
Yanxia
Wang
Department of Mathematics
Northwest Normal University
P. R. China
wangyanxia8228@163.com
Chenghua
Gao
Department of Mathematics
Northwest Normal University
P. R. China
gaokuguo@163.com
Tianmei
Geng
Department of Mathematics
Northwest Normal University
P. R. China
891459322@qq.com
Discrete fourth-order boundary value problem
multiple solutions
critical point theory
Lipschitz condition.
Article.110.pdf
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[1]
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]
Fuzzy Sumudu transform for solving fuzzy partial differential equations
Fuzzy Sumudu transform for solving fuzzy partial differential equations
en
en
In this paper, we propose a new method for solving fuzzy partial differential equation using fuzzy Sumudu
transform. First, we provide fundamental results of fuzzy Sumudu transform for fuzzy partial derivatives
and later use them to construct the solution of fuzzy partial differential equations. Finally, we demonstrate
an example to show the capability of the proposed method and present the results graphically.
3226
3239
Norazrizal Aswad Abdul
Rahman
Institute of Engineering Mathematics
Universiti Malaysia Perlis, Pauh Putra Main Campus
Malaysia
norazrizalaswad@gmail.com
Muhammad Zaini
Ahmad
Institute of Engineering Mathematics
Universiti Malaysia Perlis, Pauh Putra Main Campus
Malaysia
mzaini@unimap.edu.my
Fuzzy Sumudu transform
fuzzy partial derivative
fuzzy partial differential equation.
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Approximation of a common minimum-norm fixed point of a finite family of \(\sigma\)-asymptotically quasi-nonexpansive mappings with applications
Approximation of a common minimum-norm fixed point of a finite family of \(\sigma\)-asymptotically quasi-nonexpansive mappings with applications
en
en
In this paper, we use the iterative method proposed by Zegeye and Shahzad [H. Zegeye, N. Shahzed,
Fixed Point Theory Appl., 2013 (2013), 12 pages] which converges strongly to the common minimum-norm
fixed point of a finite family of \(\sigma\)-asymptotically quasi-nonexpansive mappings. As consequence, convergence
results to a common minimum-norm fixed point of a finite family of asymptotically nonexpansive mappings
is proved. Our result generalize and improve a recent result of Zegeye and Shahzad [H. Zegeye, N. Shahzed,
Fixed Point Theory Appl., 2013 (2013), 12 pages]. In the sequel, we apply our main result to find solution
of minimizer of a continuously Frechet-differentiable convex functional which has the minimum norm in
Hilbert spaces.
3240
3254
Hemant Kumar
Pathak
School of Studies in Mathematics
Pt. Ravishankar Shukla University
India
hkpathak05@gmail.com
Vinod Kumar
Sahu
Department of Mathematics
Govt. V.Y.T. P.G. Autonomous College
India
vksahu07@gmail.com
Yeol Je
Cho
Department of Mathematics Education and the RINS
Department of Mathematics
Gyeongsang National University
King Abdulaziz University
Korea
Saudi Arabia
yjcho@gnu.ac.kr
Asymptotically quasi-nonexpansive mappings
asymptotically nonexpansive mappings
nonexpansive mappings
minimum-norm fixed point
strong convergence.
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Generalized \(\alpha-\psi\) contractive mappings in partial b-metric spaces and related fixed point theorems
Generalized \(\alpha-\psi\) contractive mappings in partial b-metric spaces and related fixed point theorems
en
en
In this paper, we introduce some concepts in partial b-metric spaces. We establish fixed point theorems
for some new generalized \(\alpha-\psi\) type contractive mappings in the setting of partial b-metric spaces. Some
examples are presented to illustrate our obtained results. Finally, we show that the results generalize some
recent results.
3255
3278
Xianbing
Wu
Department of Mathematics
Yangzte Normal University
P. R. China
flwxbing@163.com
Contractive mapping
partial b-metric space
fixed point theorem.
Article.113.pdf
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[1]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces , Math. Slovaca, 64 (2014), 941-960
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]
Nonexistence of global weak solutions of a system of wave equations on the Heisenberg group
Nonexistence of global weak solutions of a system of wave equations on the Heisenberg group
en
en
Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudoparabolic
equation
\[u_{tt} -\Delta_{\mathbb{H}}u + (- \Delta_{\mathbb{H}})^{ \frac{\delta}{2} }u = f(\eta; t)u^p;\qquad (\eta, t) \in \mathbb{H} \times(0,\infty); p > 1;\quad u \geq 0;\]
where \( \Delta_{\mathbb{H}}\) is the Kohn{Laplace operator on the \((2N + 1)\)-dimensional Heisenberg group \(\mathbb{H}\) and \(f(\eta; t)\) is a
given function. Then, this result is extended to the case of a \(2 \times 2\)-system of the same type. Our technique
of proof is based on a duality argument.
3279
3286
Rabah
Kellil
Faculty of Science Al Zulfi
University of Majmaah
KSA
kellilrabah@yahoo.fr;r.kellil@mu.edu.sa
Mokhtar
Kirane
Laboratoire de Mathématiques, Image et Applications, Faculté des Sciences
pôle Sciences et Technologies
France
mokhtar.kirane@univ-lr.fr
Nonexistence
nonlinear hyperbolic equation
systems of hyperbolic equations
Heisenberg group.
Article.114.pdf
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[1]
B. Ahmad, A. Alsaedi, M. Kirane, Nonexistence of global solutions of some nonlinear space-nonlocal evolution equations on the Heisenberg group, Electron. J. Differential Equations, 2015 (2015), 1-10
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]
Analysis of a viral infection model with immune impairment and cure rate
Analysis of a viral infection model with immune impairment and cure rate
en
en
In this paper, the dynamics behavior of a delayed viral infection model with immune impairment and
cure rate is studied. It is shown that there exists three equilibria. By analyzing the characteristic equations,
the local stability of the infection-free equilibrium and the immune-exhausted equilibrium of the model are
established. In the following, the stability of the positive equilibrium is studied. Furthermore, we investigate
the existence of Hopf bifurcation by using a delay as a bifurcation parameter. Finally, numerical simulations
are carried out to explain the mathematical conclusions.
3287
3298
Jianwen
Jia
School of Mathematics and Computer Science
Shanxi Normal University
P. R. China
jiajw.2008@163.com
Xuewei
Shi
School of Mathematics and Computer Science
Shanxi Normal University
P. R. China
Viral infection
immune impairment
cure rate
Hopf bifurcation
stability.
Article.115.pdf
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]
Existence of solutions for generalized mixed variational inequalities in reflexive Banach spaces
Existence of solutions for generalized mixed variational inequalities in reflexive Banach spaces
en
en
This paper is devoted to the solvability of generalized mixed variational inequalities in reflexive Banach
spaces. We prove the existence of solutions of the generalized mixed variational inequalities for f-
quasimonotone set-valued mappings without any assumption on bounded values. Furthermore, we give
some conditions that guarantee the existence of solutions of the generalized mixed variational inequalities
over unbounded closed convex subsets. Our results extend and improve some recent results from the
literature.
3299
3309
Zhong-Bao
Wang
Department of Mathematics
Southwest Jiaotong University
P. R. China
zhongbaowang@hotmail.com
Zi-Li
Chen
Department of Mathematics
Southwest Jiaotong University
P. R. China
zlchen@swjtu.edu.cn
Generalized mixed variational inequality
reflexive Banach space
existence
f-quasimonotonicity.
Article.116.pdf
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K. Q. Wu, N. J. Huang, The generalized f-projection operator and set-valued variational inequalities in Banach spaces, Nonlinear Anal., 71 (2009), 2481-2490
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J. Yu, H. Yang, Existence of solutions for generalized variational inequality problems, Nonlinear Anal., 71 (2009), 2327-2330
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L. C. Zeng, J. C. Yao, Existence theorems for variational inequalities in Banach spaces, J. Optim. Theory Appl., 132 (2007), 321-337
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R. Y. Zhong, N. J. Huang, Stability analysis for minty mixed variational inequality in reflexive Banach spaces, J. Optim. Theory Appl., 147 (2010), 454-472
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R. Y. Zhong, N. J. Huang, Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces, J. Optim. Theory Appl., 152 (2012), 696-709
]
Extremal system of solutions for a coupled system of nonlinear fractional differential equations by monotone iterative method
Extremal system of solutions for a coupled system of nonlinear fractional differential equations by monotone iterative method
en
en
In this paper, we deal with a coupled system of nonlinear fractional differential equations, which involve
the Riemann-Liouville derivatives of different fractional orders. By using the monotone iterative technique
combined with the method of upper and lower solutions, we not only obtain the existence of extremal system
of solutions, but also establish iterative sequences for approximating the solutions. As an application, an
example is given to illustrate our main results.
3310
3318
Suli
Liu
School of Mathematics
Jilin University
P. R. China
liusl15@mails.jlu.edu.cn
Huilai
Li
School of Mathematics
Jilin University
P. R. China
lihuilai@jlu.edu.cn
Fractional di erential systems
monotone iterative method
iterative sequences
extremal system of solutions.
Article.117.pdf
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[1]
M. Al-Refai, M. Ali Hajji , Monotone iterative sequences for nonlinear boundary value problems of fractional order, Nonlinear Anal., 74 (2011), 3531-3539
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A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model , J. Thermal Sci., submitted (2016)
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A. Atangana, I. Koca, Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractionalorder, Chaos, Solitons and Fractals, in press (2016)
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K. Deimling, V. Lakshmikantham, Existence and comparison theorems for differential equations in Banach spaces, Nonlinear Anal., 3 (1979), 569-575
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S. Liu, H. Li, Q. Dai, Nonlinear fractional differential equations with nonlocal integral boundary conditions, Adv. Difference Equ., 2015 (2015), 1-11
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A. McBride, J. Sabatier, O. P. Agrawal, J. Machado, Advances in fractional calculus: theoretical developments and applications in physics and engineering, Springer, Dordrecht (2007)
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G. Wang, R. P. Agarwal, A. Cabada , Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations, Appl. Math. Lett., 25 (2012), 1019-1024
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G. Wang, D. Baleanu, L. Zhang, Monotone iterative method for a class of nonlinear fractional differential equations, Fract. Calc. Appl. Anal., 15 (2012), 244-252
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W. Wang, J. Tian , Generalized monotone iterative method for integral boundary value problems with causal operators, J. Nonlinear Sci. Appl., 8 (2015), 600-609
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W. Xie, J. Xiao, Z. Luo, Existence of extremal solutions for nonlinear fractional differential equation with nonlinear boundary conditions, Appl. Math. Lett., 41 (2015), 46-51
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N. Xu, W. Liu, Iterative solutions for a coupled system of fractional differential-integral equations with two-point boundary conditions , Appl. Math. Comput., 244 (2014), 903-911
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S. Zhang, Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives, Nonlinear Anal., 71 (2009), 1-2087
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X. Zhang, L. Liu, Y. Wu, Y. Lu, The iterative solutions of nonlinear fractional differential equations, Appl. Math. Comput., 219 (2013), 4680-4691
]
Improved version of perturbed Ostrowski type inequalities for \(n\)-times differentiable mappings with three-step kernel and its application
Improved version of perturbed Ostrowski type inequalities for \(n\)-times differentiable mappings with three-step kernel and its application
en
en
New integral inequalities of Ostrowski type are developed for n-times differentiable mappings by using
a 3-step kernel when either \(f^{(n)} \in L^1[a; b]\) or \(f \in L^2[a; b]\). Some new inequalities are derived as special
cases of the obtained inequalities. New efficient quadrature rules are also derived with the help of obtained
inequalities. The efficiency of the new quadrature rules is demonstrated with the help of specific examples.
Finally, applications for cumulative distribution functions is also provided.
3319
3332
A. R.
Kashif
Department of Mathematics
Capital University of Sciences and Technology
Pakistan
kashmology@gmail.com
M.
Shoaib
Abu Dhabi Mens College
Higher Colleges of Technology
United Arab Emirates
safridi@gmail.com
M. A.
Latif
School of Computational and Applied Mathematics
University of the Witwatersrand
South Africa
m_amer_latif@hotmail.com
Ostrowski inequality
Čebyšev-Grüss inequality
Čebyšev functional.
Article.118.pdf
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[1]
M. W. Alomari, A companion of Ostrowski's inequality with applications, Transylv. J. Math. Mech., 3 (2011), 9-14
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P. Cerone, S. S. Dragomir, J. Roumeliotis, Some Ostrowski type inequalities for n-times differnentiable mappings and applications , Demonstratio Math., 32 (1999), 697-712
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Uncertain Hermite-Hadamard inequality for functions with (s,m)-Godunova-Levin derivatives via fractional integral
Uncertain Hermite-Hadamard inequality for functions with (s,m)-Godunova-Levin derivatives via fractional integral
en
en
In this paper, we mix both concepts of s-Godunova-Levin and m-convexity and introduce the (s,m)-
Godunova-Levin functions. We introduce the fuzzy Hermite-Hadamard inequality for (s,m)-Godunova-Levin
functions via fractional integral. Holder inequality is used for new bounds for fuzzy Hermite-Hadamard
inequality. Then we accommodate this result with the previous works that have been done before.
3333
3347
Ladan
Avazpour
Department of Mathematics
Yasooj Branch, Islamic Azad University
Iran
avazpour.l@gmail.com
Tofigh
Allahviranloo
Department of Mathematics
Department of Mathematics and Statistics
Tehran Science and Research Branch, Islamic Azad University
University of Prince Edward Island
Iran
Canada
tofigh@allahviranloo.com
Shafiqul
Islam
Department of Mathematics and Statistics
University of Prince Edward Island
Canada
Fuzzy number
fuzzy Hermite-Hadamard inequality
s-Godunova-Levin function
m-convex function
fractional integral.
Article.119.pdf
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[1]
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]
On the existence of the mild solution for semilinear nonlocal fractional Cauchy problem
On the existence of the mild solution for semilinear nonlocal fractional Cauchy problem
en
en
We consider the nonlocal Cauchy problem for the semilinear functional differential equation with non-
integer order:
\[u^\alpha(t) = Au(t) + f(t; u_t) \,\texttt{where}\, \alpha \in (0; 1] \, \texttt{and} \, t \in (0; a],\]
\[u(\tau_k + 0) = Q_ku(\tau_k) \equiv u(\tau_k) + I_ku(\tau_k); k = 1; 2; ... ;K,\]
\[u(t) + (g(u_{t_1} ,..., u_{t_p}))(t) = \phi(t), \, \texttt{where} \, t \in [-r; 0].\]
Under suitable conditions we prove the existence and uniqueness of a mild solution to the equation.
3348
3353
Samer
Al Ghour
Department of Mathematics and Statistics
Jordan University of Science and Technology
Jordan
algore@just.edu.jo
Ahmad
Al Omari
Department of Mathematics, Faculty of Science
Al al-Bayt University
Jordan
omarimutah1@yahoo.com
Cauchy problem
mild solution
impulsive functional
fractional differential equation
fixed point.
Article.120.pdf
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[1]
J. H. Barrett, Differential equations of non-integer order, Canadian J. Math., 6 (1954), 529-541
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]
A new concept of (\(\alpha ,F_d\))-contraction on quasi metric space
A new concept of (\(\alpha ,F_d\))-contraction on quasi metric space
en
en
In the present paper, we introduce a new concept of (\(\alpha ,F_d\))-contraction on quasi metric space. Then we
provide some new fixed point theorems for such type mappings on left K, left M and left Smyth-complete
quasi metric spaces.
3354
3361
Ishak
Altun
College of Science
Department of Mathematics, Faculty of Science and Arts
King Saud University
Kirikkale University
Saudi Arabia
Turkey
ishakaltun@yahoo.com
Nasir
Al Arifi
Geology and Geophysics Department, College of Science
King Saud University
Saudi Arabia
nalarifi@ksu.edu.sa
Mohamed
Jleli
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
jleli@ksu.edu.sa
Aref
Lashin
Petroleum and Gas Engineering Department, College of Engineering
Geology Department, Faculty of Science
King Saud University
Benha University
Saudi Arabia
Egypt
su.edu.sa
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
Quasi metric space
left K-Cauchy sequence
left K-completeness
fixed point.
Article.121.pdf
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C. Alegre, J. Marín, S. Romaguera, A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-8
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M. U. Ali, T. Kamran, N. Shahzad, Best proximity point for \(\alpha-\psi\)-proximal contractive multimaps, Abstr. Appl. Anal., 2014 (2014), 1-6
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I. Altun, G. Mınak, M. Olgun, Fixed points of multivalued nonlinear F-contractions on complete metric spaces, Nonlinear Anal. Model. Control, 21 (2016), 201-210
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I. Altun, G. Mınak, M. Olgun, Classification of completeness of quasi metric space and some new fixed point results, , (Submitted), -
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I. Altun, M. Olgun, G. Mınak, On a new class of multivalued weakly Picard operators on complete metric spaces, Taiwanese J. Math., 19 (2015), 659-672
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I. Altun, M. Olgun, G. Mınak, A new approach to the Assad-Kirk fixed point theorem, J. Fixed Point Theory Appl., 18 (2016), 201-212
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S. Cobzaş, Functional analysis in asymmetric normed spaces, Birkhuser-Springer, Basel (2013)
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M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat, 28 (2014), 715-722
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G. Durmaz, G. Mınak, I. Altun, Fixed point results for \(\alpha-\psi\)-contractive mappings including almost contractions and applications, Abstr. Appl. Anal., 2014 (2014), 1-10
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N. Hussain, E. Karapınar, P. Salimi, F. Akbar, \(\alpha\)-admissible mappings and related fixed point theorems, J. Inequal. Appl., 2013 (2013), 1-11
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N. Hussain, C. Vetro, F. Vetro, Fixed point results for \(\alpha\)-implicit contractions with application to integral equations, Nonlinear Anal. Model. Control, 21 (2016), 362-378
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E. Karapınar, B. Samet, Generalized \(\alpha-\psi\)-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012), 1-17
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P. Kumam, C. Vetro, F. Vetro, Fixed points for weak \(\alpha-\psi\)-contractions in partial metric spaces, Abstr. Appl. Anal., 2013 (2013), 1-9
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G. Mınak, M. Olgun, I. Altun, A new approach to fixed point theorems for multivalued contractive maps , Carpathian J. Math., 31 (2015), 241-248
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H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
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D. Wardowski, N. Van Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math., 47 (2014), 146-155
]
Some new Grüss type quantum integral inequalities on finite intervals
Some new Grüss type quantum integral inequalities on finite intervals
en
en
In this paper, we establish some new Grüss type quantum integral inequalities on finite intervals. Furthermore,
some related quantum integral inequalities are also considered.
3362
3375
Zhen
Liu
School of Mathematics and Statistics
Kashgar University
China
lz790821ks@126.com
Wengui
Yang
Ministry of Public Education
Sanmenxia Polytechnic
China
wgyang0617@yahoo.com
Grüss type inequalities
integral inequalities
quantum calculus
finite intervals.
Article.122.pdf
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[1]
F. Ahmad, N. S. Barnett, S. S. Dragomir, New weighted Ostrowski and Čebyšev type inequalities, Nonlinear Anal., 71 (2009), 1408-1412
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P. Cerone, S. S. Dragomir, New bounds for Čebyšev functional, Appl. Math. Lett., 18 (2005), 603-611
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P. Cerone, S. S. Dragomir, A refinement of the Grüss type inequality and applications, Tamkang J. Math., 38 (2007), 37-49
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F. Chen, W. Yang, Some new Chebyshev type quantum integral inequalities on finite intervals, J. Comput. Anal. Appl., 21 (2016), 417-426
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S. S. Dragomir , Some integral inequalities of Grüss type, Indian J. Pure Appl. Math., 31 (2000), 397-415
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S. S. Dragomir , Quasi Grüss type inequalities for continuous functions of selfadjoint operators in Hilbert spaces, Filomat, 27 (2013), 277-289
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H. Gauchman, Integral inequalities in q-calculus , Comput. Math. Appl., 47 (2004), 281-300
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G. Grüss , Uber das maximum des absoluten Betrages von \(\frac{1}{ b-a} \int_ b ^a f(x)g(x)dx- \frac{ 1}{ (b-a)^2} \int _b^a f(x)dx \int_ b^a g(x)dx\), Math. Z., 39 (1935), 215-226
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A. Guezane-Lakoud, F. Aissaoui , New Čebyšev type inequalities for double integrals, J. Math. Inequal., 5 (2011), 453-462
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V. Kac, P. Cheung, Quantum calculus, Springer-Verlag, New York (2002)
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Z. Liu, W. Yang, New weighted q- Čebyšev-Grüss type inequalities for double integrals, J. Comput. Anal. Appl., 20 (2016), 938-948
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S. Marinković, P. Rajković, M. Stanković, The inequalities for some types of q-integrals , Comput. Math. Appl., 56 (2008), 2490-2498
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M. Masjed-Jamei , Inequalities for two specific classes of functions using Chebyshev functional, Filomat, 25 (2011), 153-163
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D. S. Mitrinović, J. E. Pečarić, A. M. Fink , Classical and new inequalities in analysis, Kluwer Academic Publishers, Dordrecht (1993)
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B. G. Pachpatte, On Čebyšev-Grüss type inequalities via Pečarić's extension of the montgomery identity, J. Inequal. Pure Appl. Math., 7 (2006), 1-10
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B. G. Pachpatte, New inequalities of Čebyšev type for double integrals , Demonstratio Math., 40 (2007), 43-50
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W. Sudsutad, S. K. Ntouyas, J. Tariboon , Fractional integral inequalities via Hadamard's fractional integral, Abstr. Appl. Anal., 2014 (2014), 1-11
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J. Tariboon, S. K. Ntouyas , Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ., 2013 (2013), 1-19
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J. Tariboon, S. K. Ntouyas, W. Sudsutad, Some new Riemann-Liouville fractional integral inequalities, Int. J. Math. Math. Sci., 2014 (2014), 1-6
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J. Tariboon, S. K. Ntouyas , Quantum integral inequalities on finite intervals, J. Inequal. Appl., 2014 (2014), 1-13
##[24]
S. Wu , A new sharpened and generalized version of Hölder's inequality and its applications, Appl. Math. Comput., 197 (2008), 708-714
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S. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications, Rocky Mountain J. Math., 39 (2009), 1741-1749
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W. Yang, On weighted q- Čebyšev-Grüss type inequalities, Comput. Math. Appl., 61 (2011), 1342-1347
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W. Yang, On two dimensional q-Hölder's inequality, Kyungpook Math. J., 52 (2012), 397-404
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W. Yang, Some new Chebyshev and Güss-type integral inequalities for Saigo fractional integral operators and their q-analogues, Filomat, 29 (2015), 1269-1289
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C. Zhu, W. Yang, Q. Zhao, Some new fractional q-integral Grüss-type inequalities and other inequalities, J. Inequal. Appl., 2012 (2012), 1-15
]
Certain inequalities involving generalized fractional \(k\)-integral operators
Certain inequalities involving generalized fractional \(k\)-integral operators
en
en
Recently, fractional k-integral operators have been investigated in the literature by some authors. Here,
we focus to prove some new fractional integral inequalities involving generalized fractional k-integral operator
due to Sarikaya et al. for the cases of synchronous functions as well as of functions bounded by integrable
functions are considered.
3376
3387
K. S.
Nisar
Department of Mathematics, College of Arts and Science
Prince Sattam bin Abdulaziz University
Saudi Arabia
ksnisar1@gmail.com
M.
Al-Dhaifallah
Department of Electrical Engineering, College of Engineering-Wadi AlDawaser
Prince Sattam bin Abdulaziz University
Saudi Arabia
m.aldhaifallah@psau.edu.sa
M. S.
Abouzaid
Department of Mathematics, Faculty of Science
Kafrelsheikh University
Egypt
moheb_abouzaid@hotmail.com
P.
Agarwal
Department of Mathematics
Anand International College of Engineering
India
goyal.praveen2011@gmail.com
Coincidence point
common fixed point
contraction
implicit relation
partial metric space.
Article.123.pdf
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[1]
P. Agarwal, J. Choi , Certain fractional integral inequalities associated with Pathway fractional integral operators, Bull. Korean Math. Soc., 53 (2016), 181-193
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P. Agarwal, S. S. Dragomir, J. Park, S. Jain, q-Integral inequalities associated with some fractional q-integral operators, J. Inequal. Appl., 2015 (2015), 1-13
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P. Agarwal, J. Tariboon, S. K. Ntouyas, Some generalized Riemann-Liouville k-fractional integral inequalities, J. Inequal. Appl., 2016 (2016), 1-13
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A. Alsaedi, D. Baleanu, S. Etemad, S. Rezapour, On coupled systems of time-fractional differential problems by using a new fractional derivative, J. Funct. Spaces, 2016 (2016), 1-8
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G. A. Anastassiou, Advances on Fractional Inequalities, Springer Briefs in Mathematics, Springer, New York (2011)
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A. Atangana, On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation, Appl. Math. Comput., 273 (2016), 948-956
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A. Atangana, D. Baleanu, CaputoFabrizio derivative applied to groundwater flow with in a confined aquifer, J. Eng. Mech., 2016 (2016)
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A. Atangana, D. Baleanu, New fractional derivatives with non local and non-singular kernel:theory and application to heat transfer model, arXiv preprint , arXiv:1602.03408 (2016)
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S. Belarbi, Z. Dahmani , On some new fractional integral inequalities, JIPAM. J. Inequal. Pure Appl. Math., 10 (2009), 1-5
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J. Choi, P. Agarwal, Some new Saigo type fractional integral inequalities and their q-analogues, Abstr. Appl. Anal., 2014 (2014), 1-11
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S. S. Dragomir, Some integral inequalities of Gruss type, Indian J. Pure Appl. Math., 31 (2000), 397-415
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]
Some identities for the generalized Laguerre polynomials
Some identities for the generalized Laguerre polynomials
en
en
In this paper, we perform a further investigation for the generalized Laguerre polynomials. By applying
the generating function methods and Padé approximation techniques, we establish some new identities for the
generalized Laguerre polynomials, and give some illustrative special cases as well as immediate consequences
of the main results.
3388
3396
Wen-Kai
Shao
Department of Mathematical Teaching and Research
Yibin Vocational & Technical College
P. R. China
wksh 0@163.com
Yuan
He
Faculty of Science
Kunming University of Science and Technology
P. R. China
hyyhe@aliyun.com;hyyhe@outlook.com
Jing
Pan
Faculty of Science
Kunming University of Science and Technology
P. R. China
panjing320@sina.com
Generalized Laguerre polynomials
Padé approximation
combinatorial identities.
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Algorithms for common solutions of generalized mixed equilibrium problems and system of variational inclusion problems
Algorithms for common solutions of generalized mixed equilibrium problems and system of variational inclusion problems
en
en
In this paper, we introduce a multi-step iterative algorithm for finding a common element of the set of
solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family
of variational inclusions for maximal monotone and inverse strong monotone mappings, the set of solutions
of general system of variational inequalities and the set of fixed points of a countable family of nonexpansive
mappings in a real Hilbert space. This multi-step iterative algorithm is based on Korpelevich's extragradient
method, viscosity approximation method, projection method, and strongly positive bounded linear
operator and W-mapping approaches. We establish the strong convergence of the sequences generated by
the proposed algorithm to a common element of above mentioned problems under appropriate assumptions,
which also solves some optimization problem. The result presented in this paper improves and extends some
corresponding ones in the earlier and recent literature.
3397
3423
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities
China
zenglc@hotmail.com
A.
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
A. E.
Al-Mazrooei
Department of Mathematics
University of Jeddah
Saudi Arabia
aealmazrooei@kau.edu.sa
Multi-step iterative algorithm
mixed equilibrium problem
Variational inclusion
nonexpansive mapping
maximal monotone mapping
strong convergence.
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]
Optimal bounds for a Toader-type mean in terms of one-parameter quadratic and contraharmonic means
Optimal bounds for a Toader-type mean in terms of one-parameter quadratic and contraharmonic means
en
en
In this paper, we present the best possible Toader mean bounds of arithmetic and quadratic means by
the one-parameter quadratic and contraharmonic means. As applications in engineering and technology, we
find new bounds for the complete elliptic integral of the second kind.
3424
3432
Hong-Hu
Chu
School of Civil Engineering and Architecture
Changsha University of Science & Technology
China
chuhonghu2005@126.com
Wei-Mao
Qian
School of Distance Education
Huzhou Broadcast and TV University
China
qwm661977@126.com
Yu-Ming
Chu
School of Mathematics and Computation Science
Hunan City University
China
chuyuming2005@126.com
Ying-Qing
Song
School of Mathematics and Computation Science
Hunan City University
China
1452225875@qq.com
Toader mean
arithmetic mean
quadratic mean
contraharmonic mean
complete elliptic integral.
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]
Infinitely many solutions to boundary value problems for a coupled system of fractional differential equations
Infinitely many solutions to boundary value problems for a coupled system of fractional differential equations
en
en
Using the variational methods, we investigate the solutions to the boundary value problems for a coupled
system of fractional order differential equations. First, we obtain the existence of at least one weak solution
by the minimization result due to Mawhin and Willem. Then, the existence criteria of infinitely many
solutions are established by a critical point theorem due to Rabinowitz. At last, some examples are also
provided to illustrate the results.
3433
3444
Peiluan
Li
School of Mathematics and Statistics
Henan University of Science and Technology
P. R. China
lpllpl_lpl@163.com
Hui
Wang
College of Information Engineering
Henan University of Science and Technology
P. R. China
wh@haust.edu.cn
Zheqing
Li
Network and Information Center
Henan University of Science and Technology
P. R. China
lzq@haust.edu.cn
Fractional differential equations
coupled system
variational method
infinitely many solutions.
Article.127.pdf
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B. Ahmad, A. Alsaedi , Existence and uniqueness of solutions for coupled systems of higher-order nonlinear fraction differential equations, Fixed Point Theory Appl., 2010 (2010), 1-17
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J. Chen, X. H. Tang , Existence and multiplicity of solutions for some fractional boundary value problem via critical point theory, Abstr. Appl. Anal., 2012 (2012), 1-21
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J. Graef, L. Kong, Positive solutions for a class of higher order boundary value problems with fractional q- derivatives , Appl. Math. Comput., 218 (2012), 9682-9689
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Y. Liu, W. Zhang, X. Liu, A sufficient condition for the existence of a positive solution for a nonlinear fractional differential equation with the Riemann-Liouville derivative, Appl. Math. Lett., 25 (2012), 1986-1992
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]
On common fixed points for \(\alpha-F\)-contractions and applications
On common fixed points for \(\alpha-F\)-contractions and applications
en
en
In this paper, we introduce the concept of modified F-contractions via \(\alpha\)-admissible pair of mappings.
We also provide several common fixed point results in the setting of metric spaces. Moreover, we present
some illustrated examples and we give two applications on a dynamic programming and an integral equation.
3445
3458
Ahmed
Al-Rawashdeh
Department of Mathematical Sciences
UAE University
UAE
aalrawashdeh@uaeu.ac.ae
Hassen
Aydi
Department of Mathematics
Department of Medical Research
College of Education of Jubail, University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Abdelbasset
Felhi
Department of Mathematics and Statistics, College of Sciences
King Faisal University
Saudi Arabia
afelhi@kfu.edu.sa
Slah
Sahmim
Department of Mathematics and Statistics, College of Sciences
King Faisal University
Saudi Arabia
ssahmim@kfu.edu.sa
Wasfi
Shatanawi
Department of Mathematics and General Courses
Department of Mathematics
Prince Sultan University
The Hashemite University
KSA
Jordan
wshatanawi@psu.edu.sa
Metric space
\(\alpha\)-admissible mappings
F-contraction
common fixed point.
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[1]
J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized F-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-18
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H. Aydi, Coincidence and common fixed point results for contraction type maps in partially ordered metric spaces, Int. J. Math. Anal., 5 (2011), 631-642
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H. Aydi, \(\alpha\)-implicit contractive pair of mappings on quasi b-metric spaces and application to integral equations, Accepted in J. Nonlinear Convex Anal., (2015)
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H. Aydi, M. Jellali, E. Karapınar, On fixed point results for \(\alpha\)-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21 (2016), 40-56
##[5]
H. Aydi, E. Karapınar, Fixed point results for generalized \(\alpha-\psi\)-contractions in metric-like spaces and applications, Electron. J. Differential Equations, 2015 (2015), 1-15
##[6]
H. Aydi, H. K. Nashine, B. Samet, H. Yazidi, Coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations, Nonlinear Anal., 74 (2011), 6814-6825
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B. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math., 3 (1922), 133-181
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L. B. Budhia, P. Kumam, J. Martínez-Moreno, D. Gopal, Extensions of almost-F and F-Suzuki contractions with graph and some applications to fractional calculus, Fixed Point Theory Appl., 2016 (2016), 1-14
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M. Jleli, E. Karapınar, B. Samet, Best proximity points for generalized \(\alpha-\psi\)-proximal contractive type mappings, J. Appl. Math., 2013 (2013), 1-10
##[13]
M. Jleli, E. Karapınar, B. Samet , Fixed point results for \(\alpha-\psi_\lambda\) contractions on gauge spaces and applications, ,Abstr. Appl. Anal., 2013 (2013), 1-7
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M. Jleli, B. Samet, C. Vetro, F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstr. Appl. Anal., 2015 (2015), 1-7
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E. Karapınar, B. Samet, Generalized \(\alpha-\psi\) -contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012), 1-17
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D. Klim, D. Wardowski , Fixed points of dynamic processes of set-valued F-contractions and application to functional equations, Fixed Point Theory Appl., 2015 (2015), 1-9
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J. J. Nieto, R. Rodríguez-López, Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations, Order, 22 (2005), 223-239
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D. Paesano, C. Vetro, Multi-valued F-contractions in 0-complete partial metric spaces with application to Volterra type integral equation, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math., 108 (2014), 1005-1020
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H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
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A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2003), 1435-1443
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B. Samet, C. Vetro, P. Vetro , Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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M. Sgroi, C. Vetro, Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat, 27 (2013), 1259-1268
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W. Shatanawi, A. Al-Rawashdeh, Common fixed points of almost generalized ( \(\psi,\phi\))-contractive mappings in ordered metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-14
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