]>
2017
10
9
ISSN 2008-1898
579
Some new fractional integral inequalities for \(s\)-convex functions
Some new fractional integral inequalities for \(s\)-convex functions
en
en
In this paper, a similar equality which is given in [C. Yildiz, M. E.Ozdemir, M. Z. Sarikaya, Kyungpook Math. J., \({\bf 56}\) (2016), 161--172] is proved
by using different symbols and impressions. By using this equality, some new
fractional integral inequalities for \(s\)-convex functions are obtained. Also, some applications to special means of positive real numbers are given. If the \(\alpha=1\) is taken, our results coincide with the results given in [E. Set, M. E. Ozdemir, M. Z. Sarikaya, Facta Unv. Ser. Math. Inform., \({\bf 27}\) (2012), 67--82]\) so our results are more general from the results given there.
4552
4563
Dunya
Karapinar
Department of Mathematics, Faculty of Sciences
Karadeniz Technical University
Turkey
dunyakarapinar@ktu.edu.tr
Sercan
Turhan
Department of Mathematics, Faculty of Sciences and Arts
Giresun University
Turkey
sercan.turhan@giresun.edu.tr
Mehmet
Kunt
Department of Mathematics, Faculty of Sciences
Karadeniz Technical University
Turkey
mkunt@ktu.edu.tr
Imdat
Iscan
Department of Mathematics, Faculty of Sciences and Arts
Giresun University
Turkey
imdat.iscan@giresun.edu.tr
Ostrowski type inequalities
midpoint type inequalities
Riemann-Liouville fractional integrals
s-convex functions.
Article.1.pdf
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[1]
M. Alomari, M. Darus, Some Ostrowski’s type inequalities for convex functions with applications, RGMIA Res. Rep. Coll, 2010 (2010), 1-14
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M. Alomari, M. Darus, S. S. Dragomir, P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett., 23 (2010), 1071-1076
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M. Alomari, M. Darus, U. S. Kırmacı , Some inequalities of Hermite-Hadamard type for s-convex functions , Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 1643-1652
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D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo , Fractional Calculus: Models and Numerical Methods, World Scientific, Singapore (2012)
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S. S. Dragomir, S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math., 32 (1999), 687-696
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S. S. Dragomir, T. M. Rassias, Ostrowski type inequalities and applications in numerical integration, Springer, Netherlands (2000)
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G. Farid, Some new Ostrowski type inequalities via fractional integrals, Int. J. Anal. Appl., 14 (2017), 64-68
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H. Hudzik, L. Maligranda , Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100-111
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İ. İşcan , Ostrowski type inequalities for harmonically s-convex functions, Konuralp J. Math., 3 (2015), 63-74
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İ. İşcan , Ostrowski type inequalities for p-convex functions , New trends Math. Sci., 4 (2016), 140-150
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Amsterdam (2006)
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M. A. Latif, S. S. Dragomir, A. E. Matouk, New inequalities of Ostrowski type for co-ordinated s-convex functions via fractional integrals, J. Frac. Calcu. Appl., 4 (2013), 22-36
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M. Matloka, Ostrowski type inequalities for functions whose derivatives are h-convex via fractional integrals, J. Sci. Res. & Rep., 3 (2014), 1633-1641
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A. Ostrowski, Über die Absolut abweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Hel, 10 (1938), 226-227
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M. Z. Sarıkaya, H. Budak, Generalized Ostrowski type inequalities for local fractional integrals , Proceed. Amer. Math. Soc., 145 (2017), 1527-1538
##[16]
E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals, Comp. Math. Appl., 63 (2012), 1147-1154
##[17]
E. Set, M. E. Özdemir, M. Z. Sarıkaya, New inequalities of Ostrowskı’s type for s-convex functions in the second sense with applications, Facta Unv. Ser. Math. Inform., 27 (2012), 67-82
##[18]
C . Yıldız, M. E. Özdemir, M. Z. Sarıkaya, New Generalizations of Ostrowski-Like Type Inequalities for Fractional Integrals, Kyungpook Math. J., 56 (2016), 161-172
]
A fixed point theorem for F-Khan-contractions on complete metric spaces and application to integral equations
A fixed point theorem for F-Khan-contractions on complete metric spaces and application to integral equations
en
en
In this article, we introduce a new concept of contraction called
F-Khan-contractions and prove a fixed point theorem concerning
this contraction which generalizes the results announced by Khan
[M. S. Khan, Rend. Inst. Math. Univ. Trieste., \({\bf 8}\) (1976), 69--72], Fisher [B. Fisher, Riv. Math. Univ. Parma., \({\bf 4}\) (1978), 135--137], and Piri et al. [H. Piri, S. Rahrovi, P. Kumam, J. Math. Computer Sci., \({\bf 17}\) (2017), 76--83]. An example and application for the solution of certain integral equations are given to illustrate the usability of the obtained results.
4564
4573
Hossein
Piri
Department of mathematics
University of Bonab
Iran
h.piri@bonabu.ac.ir
Samira
Rahrovi
Department of mathematics
University of Bonab
Iran
s.rahrovi@bonabu.ac.ir
Hamidreza
Marasi
Department of applied mathematics, Faculty of mathematical sciences
University of Tabriz
Iran
Hamidreza.marasi@gmail.com
Poom
Kumam
KMUTT Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science
Department of Medical Research, China Medical University Hospital
King Mongkut's University of Technology Thonburi (KMUTT)
King Mongkuts University of Technology Thonburi (KMUTT)
China Medical University
Thailand
Thailand
Taiwan
poom.kumam@mail.kmutt.ac.th
Fixed point
metric space
integral equations.
Article.2.pdf
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[1]
M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat, 28 (2014), 715-722
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D. Dukić, Z. Kadelburg, S. Radenović , Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstr. Appl. Anal., 2011 (2011), 1-13
##[3]
N. V. Dung, V. T. L. Hang, A Fixed Point Theorem for Generalized F-Contractions on Complete Metric Spaces, Vietnam J. Math., 43 (2015), 743-753
##[4]
B. Fisher , On a theorem of Khan, Riv. Math. Univ. Parma., 4 (1978), 135-137
##[5]
M. A. Geraghty , On contractive maps, Proc. of Amer. Math. Soc., 40 (1973), 604-608
##[6]
M. S. Khan , A fixed point theorem for metric spaces, Rend. Inst. Math. Univ. Trieste., 8 (1976), 69-72
##[7]
P. Kumam, D. Gopal, L. Budhia , A new fixed point theorem under Suzuki type Z-contraction mappings, J. Math. Anal., 8 (2017), 113-119
##[8]
H. Piri, S. Rahrovi, P. Kumam , Generalization of Khan fixed point theorem, J. Math. Computer Sci., 17 (2017), 76-83
##[9]
D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces, Fixed PoinTheory Appl., 2012 (2012), 1-6
##[10]
F. Zabihi, A. Razani , Fixed point theorems for hybrid rational Geraghty contractive mappings in ordered b-metric spaces, J. Math. Appl., 2014 (2014), 1-9
]
Convergence and some control conditions of hybrid steepest-descent methods for systems of variational inequalities and hierarchical variational inequalities
Convergence and some control conditions of hybrid steepest-descent methods for systems of variational inequalities and hierarchical variational inequalities
en
en
The purpose of this paper is to find a solution of a general system of variational inequalities (for short,
GSVI), which is also a unique solution of a hierarchical variational inequality (for short, HVI) for an infinite family of
nonexpansive mappings in Banach spaces. We introduce general implicit and
explicit iterative algorithms, which are based on the hybrid steepest-descent method and the Mann iteration method. Under
some appropriate conditions, we prove the strong convergence of the sequences generated by the proposed iterative algorithms
to a solution of the GSVI, which is also a unique solution of the HVI.
4574
4596
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics, Center for Big Data Analytics \& Intelligent Healthcare, and Research Center of Nonlinear Analysis and Optimization
Department of Medical Research
Kaohsiung Medical University
Kaohsiung Medical University Hospital
Taiwan
Taiwan
simplex_liou@hotmail.com
Ching-Feng
Wen
Center for Fundamental Science
Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
Ching-Hua
Lo
Center for Big Data Analytics \& Intelligent Healthcare
Kaohsiung Medical University
Taiwan
bde_lo@sina.com
System of variational inequalities
nonexpansive mapping
fixed point
hybrid steepest-descent method
global convergence.
Article.3.pdf
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K. Aoyama, H. Iiduka, W. Takahashi, Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory Appl., 2006 (2006), 1-13
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N. Buong, N. T. H. Phuong, Strong convergence to solutions for a class of variational inequalities in Banach spaces by implicit iteration methods, J. Optim. Theory Appl., 159 (2013), 399-411
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L. C. Ceng, Q. H. Ansari, J. C. Yao , Mann-type steepest-descent and modified steepest-descent methods for variational inequalities in Banach spaces, Numer. Funct. Anal. Optim., 29 (2008), 987-1033
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L. C. Ceng, H. Gupta, Q. H. Ansari , Implicit and explicit algorithms for a system of nonlinear variational inequalities in Banach spaces, J. Nonlinear Convex Anal., 16 (2015), 965-984
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L. C. Ceng, S. M. Guu, J. C. Yao, Hybrid iterative method for finding common solutions of generalized mixed equilibrium and fixed point problems , Fixed Point Theory Appl., 2012 (2012), 1-19
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L. C. Ceng, C. F. Wen, Y. Yao, Iteration approaches to hierarchical variational inequalities for infinite nonexpansive mappings and finding zero points of m-accretive operators, J. Nonlinear Var. Anal., 1 (2017), 213-235
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S. Y. Cho, B. A. Bin Dehaish, X. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427-438
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H. K. Xu , Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
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Y.-H. Yao, R.-D. Chen, H.-K. Xu , Schemes for finding minimum-norm solutions of variational inequalities, Nonlinear Anal., 72 (2010), 3447-3456
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H. Y. Zhou, L. Wei, Y. J. Cho, Strong convergence theorems on an iterative method for a family of finite nonexpansive mappings in reflexive Banach spaces, Appl. Math. Comput., 173 (2006), 196-212
]
Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion
Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion
en
en
In this paper, we consider a class of stochastic age-dependent capital system
with fractional Brownian motion,
and investigate the convergence of numerical approximate solution. It is proved that the numerical approximation
solutions converge to the analytic solutions of the equations under given conditions. A numerical example
is provided to illustrate the theoretical results.
4597
4610
Lai-Yun
Zheng
School of Mechanical Engineering
Ningxia University
China
zhenglaiyun@126.com
Qi-Min
Zhang
School of Mathematics and Statistics
Ningxia University
China
zhangqimin64@sina.com
Stochastic age-dependent capital system
numerical solution
Euler approximation
fractional Brownian motion.
Article.4.pdf
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[1]
J. F. Coeurjolly , Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study, J. Stat. Softw., 5 (2000), 1-53
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Q.-H. Du, C.-L. Wang , Convergence analysis of semi-implicit Euler methods for solving stochastic age-dependent capital system with variable delays and random jump magnitudes , Math. Probl. Eng., 2014 (2014), 1-12
##[3]
T. E. Duncan, B. Maslowski, B. Pasik-Duncan, Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise, Stochastic Process. Appl., 115 (2005), 1357-1383
##[4]
G. Feichtinger, R. F. Hartl, P. M. Kort, V. M. Veliov , Anticipation effects of technological progress on capital accumulation: a vintage capital approach, J. Econom. Theory, 126 (2006), 143-164
##[5]
G. Feichtinger, R. F. Hartl, P. M. Kort, V. M. Veliov , Vladimir, Capital accumulation under technological progress and learning: a vintage capital approach , Eur. J. Oper. Res., 172 (2006), 293-310
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R. U. Goetz, N. Hritonenko, Y. Yatsenko, The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning , J. Econom. Dynam. Control, 32 (2008), 3032-3053
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H. Gu, J.-R. Liang, Y.-X. Zhang, Time-changed geometric fractional Brownian motion and option pricing with transaction costs, Phys. A, 391 (2012), 3971-3977
##[8]
K. Jańczak-Borkowska , Generalized BSDEs driven by fractional Brownian motion, Statist. Probab. Lett., 83 (2013), 805-811
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Y.-M. Jiang, X.-C. Wang, Y.-J. Wang, On a stochastic heat equation with first order fractional noises and applications to finance, J. Math. Anal. Appl., 396 (2012), 656-669
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P. E. Kloeden, E. Platen, Numerical solution of stochastic differential equations, Applications of Mathematics (New York), Springer-Verlag, Berlin (1992)
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W.-J. Ma, Q.-M. Zhang, C.-Z. Han, Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1884-1893
##[12]
A. Rathinasamy , Split-step \(\theta\)-methods for stochastic age-dependent population equations with Markovian switching, Nonlinear Anal. Real World Appl., 13 (2012), 1334-1345
##[13]
L. Ronghua, P.Wan-kai, L. Ping-kei , Convergence of numerical solutions to stochastic age-structured population equations with diffusions and Markovian switching, Appl. Math. Comput., 216 (2010), 744-752
##[14]
S. Rostek, R. Schöbel , A note on the use of fractional Brownian motion for financial modeling, Econ. Model., 30 (2013), 30-35
##[15]
J. Wang, J.-R. Liang, L.-J. Lv, W.-Y. Qiu, F.-Y. Ren, Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime, Phys. A, 391 (2012), 750-759
##[16]
W.-L. Xiao, W.-G. Zhang, X.-L. Zhang, Y.-L. Wang , Pricing currency options in a fractional Brownian motion with jumps, Econ. Model., 27 (2010), 935-942
##[17]
W.-L. Xiao, W.-G. Zhang, X.-L. Zhang, X.-L. Zhang , Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm, Phys. A, 391 (2012), 6418-6431
##[18]
Q.-M. Zhang , Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion, J. Comput. Appl. Math., 220 (2008), 22-33
##[19]
Q.-M. Zhang, C.-Z. Han , Numerical analysis for stochastic age-dependent population equations, Appl. Math. Comput., 169 (2005), 278-294
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Q.-M. Zhang, Y.-T. Liu, X.-N. Li , Strong convergence of split-step backward Euler method for stochastic age-dependent capital system with Markovian switching, Appl. Math. Comput., 235 (2014), 439-453
##[21]
Q.-M. Zhang, W.-K. Pang, P.-K. Leung , Exponential stability of numerical solutions for a class of stochastic age-dependent capital system with Poisson jumps , J. Comput. Appl. Math., 235 (2011), 3369-3377
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Q.-M. Zhang, A. Rathinasamy, Convergence of numerical solutions for a class of stochastic age-dependent capital system with random jump magnitudes, Appl. Math. Comput., 219 (2013), 7297-7305
]
Viscosity implicit iterative algorithms based on generalized contractions for strictly pseudo-contractive mappings in Banach spaces
Viscosity implicit iterative algorithms based on generalized contractions for strictly pseudo-contractive mappings in Banach spaces
en
en
In this manuscript, we construct three viscosity implicit iteration schemes based on generalized contractions for strictly
pseudo-contractive mappings. The first scheme is used to approximate a fixed point of a single strictly
pseudo-contractive mapping, the second scheme is used to approximate a common fixed point of a finite family of strictly
pseudo-contractive mappings, the third scheme is used to approximate a common fixed point of a countable family of strictly
pseudo-contractive mappings. Furthermore, three strong convergence
theorems based on the purposed iterative schemes are established in the framework of Banach
spaces. Finally, three numerical examples are also given to show the efficiency and implementation of our schemes. The main results of this paper modify and improve many important recent results in the literature.
4611
4627
Qingqing
Cheng
Department of Mathematics and LPMC
Nankai University
China
chengqingqing2006@126.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
China
suyongfu@tjpu.edu.cn
Strictly pseudo-contraction
implicit iterative algorithm
viscosity technique
generalized contraction
fixed point.
Article.5.pdf
[
[1]
M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H.K. Xu , The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), 1-9
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G. Bader, P. Deuhard, A semi-implicit mid-point rule for stiff systems of ordinary differential equations, Numer. Math., 41 (1983), 373-398
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Q.-W. Fan, X.-Y. Wang , An explicit iterative algorithm for k-strictly pseudo-contractive mappings in Banach spaces, J. Nonlinear Sci. Appl., 9 (2016), 5021-5028
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Y. Ke, C. Ma , The generalized viscosity implicit rules of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-21
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T. C. Lim, On characterizations of Meir-Keeler contractive maps , Nonlinear Anal., 46 (2001), 113-120
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A. Moudafi , Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55
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T. Suzuki , Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semi-groups without Bochner integrals, J. Math. Anal. Appl., 305 (2005), 227-239
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T. Suzuki , Moudafi’s viscosity approximations with Meir-Keeler contractions, J. Math. Anal. Appl., 325 (2007), 342-352
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W. Takahashi , Nonlinear Functional Analysis, Yokohama Publishers, Yokohama (2000)
##[17]
H.-K. Xu , Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[18]
H.-K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-12
##[19]
Q. Yan, G. Cai, P. Luo, Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces, J. Nonlinear Sci. Appl., 9 (2016), 4039-4051
##[20]
Y. Yao, N. Shahzad, Y. C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015), 1-15
]
On a new class of \((j, i)\)-Symmetric function on conic regions
On a new class of \((j, i)\)-Symmetric function on conic regions
en
en
In this article, a new class of functions is defined using the concepts of \((j, i)\)-symmetric functions and Janowski
functions in conic regions. Certain interesting coefficient inequalities are discussed.
4628
4637
Saqib
Hussain
COMSATS Institute of Information Technology
Pakistan
saqib_math@yahoo.com
Mohammed Ali
Alamri
School of Mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
alamri62612@gmail.com
Maslina
Darus
School of Mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
maslina@ukn.edu.my
Analytic functions
subordination
conic domain
symmetric functions.
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F. S. M. Al Sarari, S. Latha, Conic regions and symmetric points, Int. J. Pure. Appl. Math., 97 (2014), 273-285
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F. S. M. Al Sarari, S. Latha, A note on coefficient inequalities for (j, i)-symmetrical functions with conic regions, Bull. Int. Math. Virtual Inst., 6 (2016), 77-87
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]
A Bernstein polynomial approach for solution of nonlinear integral equations
A Bernstein polynomial approach for solution of nonlinear integral equations
en
en
In this study, a collocation method based on the generalized Bernstein
polynomials is derivated for solving nonlinear Fredholm-Volterra integral
equations (FVIEs) in the most general form via the quasilinearization
technique. Moreover, quadratic convergence and error estimate of the
proposed method is analyzed. Some examples are also presented to show the
accuracy and applicability of the method. keywords
4638
4647
Nese Isler
Acar
Department of Mathematics, Faculty of Arts and Sciences
Mehmet Akif Ersoy University
Turkey
nisler@mehmetakif.edu.tr
Aysegul
Dascioglu
Department of Mathematics, Faculty of Arts and Sciences
Pamukkale University
Turkey
aakyuz@pau.edu.tr
Bernstein polynomial approach
nonlinear integral equations
quasilinearization technique
collocation method.
Article.7.pdf
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K. I. Joy, Bernstein polynomials, On-Line Geometric Modeling Notes , Visualization and Graphics Research Group, Department of Computer Science, University of California, Davis, (2000), 1-13
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]
On the periodicity of a max-type rational difference equation
On the periodicity of a max-type rational difference equation
en
en
This paper shows that every well-defined solution of the following max-type difference equation
\[{x_{n + 1}} = \max \{ \frac{A}{{{x_n}}},\,\frac{A}{{{x_{n - 1}}}},\,{x_{n - 2}}\} ,\quad n \in {N_0},\]
where \(A \in R\) and the initial conditions \({x_{ - 2}},\,{x_{ - 1}},\,{x_0}\) are arbitrary non-zero real numbers is eventually periodic with period three by using new iteration method for the more general nonlinear difference equations and inequality skills as well as the mathematical induction. Our main results considerably improve results appearing in the literature.
4648
4661
Changyou
Wang
School of Applied Mathematics
College of Science
Chengdu University of Information Technology
Chongqing University of Posts and Telecommunications
P. R. China
P. R. China
wangcy@cqupt.edu.cn
Xiaotong
Jing
College of Science
Chongqing University of Posts and Telecommunications
P. R. China
Xiaohong
Hu
College of Science
Chongqing University of Posts and Telecommunications
P. R. China
Rui
Li
College of Automation
Chongqing University of Posts and Telecommunications
P. R. China
liruimath@qq.com
Max-type
difference equation
positive solution
periodic solution.
Article.8.pdf
[
[1]
M. M. El-Dessoky , On the periodicity of solutions of max-type difference equation , Math. Methods Appl. Sci., 38 (2015), 3295-3307
##[2]
E. M. Elsayed, B. Iričanin, S. Stević, On the max-type equation \(x_{n+1} = max\{\frac{A_n}{x_n} , x_{n-1}\}\) , Ars Combin., 95 (2010), 187-192
##[3]
E. M. Elsayed, S. Stević, On the max-type equation \(x_{n+1} = max\{\frac{A}{x_n} , x_{n-2}\}\), Nonlinear Anal., 71 (2009), 910-922
##[4]
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T. F. Ibrahim, N. Touafek, Max-type system of difference equations with positive two-periodic sequences, Math. Methods Appl. Sci., 37 (2014), 2541-2553
##[6]
B. D. Iričanin, E. M. Elsayed , On the max-type difference equation \(x_{n+1} = max\{\frac{A}{x_n} , x_{n-3}\}\) , Discrete Dyn. Nat. Soc., 2010 (2010), 1-13
##[7]
W. T. Jamieson, O. Merino , Asymptotic behavior results for solutions to some nonlinear difference equations, J. Math. Anal. Appl., 430 (2015), 614-632
##[8]
D. Jana, E. M. Elsayed, Interplay between strong Allee effect, harvesting and hydra effect of a single population discrete-time system, Int. J. Biomath., 9 (2016), 1-25
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B. Qin, T.-X. Sun, H.-J. Xi , Dynamics of the max-type difference equation \(x_{n+1} = max\{\frac{A}{x_n} , x_{n-k}\}\) , J. Comput. Anal. Appl., 14 (2012), 856-861
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Q. Xiao, Q.-H. Shi, Eventually periodic solutions of a max-type equation, Math. Comput. Modelling, 57 (2013), 992-996
]
Investigating dynamical behaviors of the difference equation \(x_{n+1}= \frac{Cx_{n-5}}{A+Bx_{n-2}x_{n-5}}\)
Investigating dynamical behaviors of the difference equation \(x_{n+1}= \frac{Cx_{n-5}}{A+Bx_{n-2}x_{n-5}}\)
en
en
In this work, we investigate the dynamical behaviors of the rational
difference equation%
\[
x_{n+1}=\frac{Cx_{n-5}}{A+Bx_{n-2}x_{n-5}},
\]
with arbitrary initial conditions, where \(A,\ B\), and \(C\) are arbitrary
constants. A general solution is obtained. Asymptotic behavior and
asymptotic stability of the equilibrium points are investigated. The
existence of the periodic solutions is discussed. Numerical simulations are
carried out to verify the analytical results.
4662
4679
M.
Ghazel
Mathematics Department, Faculty of Science
University of Hail
Saudi Arabia
malek_-ghazel@yahoo.fr
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. E.
Matouk
Mathematics Department, Faculty of Science
University of Hail
Saudi Arabia
aematouk@hotmail.com
A. M.
Mousallam
Mathematics Department, Faculty of Science
University of Hail
Saudi Arabia
ahmedmetwally77@hotmail.com
Rational difference equations
asymptotic behavior
infinite products
local stability
periodicity
convergence.
Article.9.pdf
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[1]
H. N. Agiza, A. A. Elsadany, Chaotic dynamics in nonlinear duopoly game with heterogeneous players, Appl. Math. Comput., 149 (2004), 843-860
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C. Cinar , On the difference equation \(x_{n+1} = \frac{x_{n-1}}{ -1+x_nx_{n-1}}\) , Appl. Math. Comput., 158 (2004), 813-816
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E. M. Elabbasy, A. A. Elsadany, Y. Zhang , Bifurcation analysis and chaos in a discrete reduced Lorenz system, Appl. Math. Comput., 228 (2014), 184-194
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M. M. El-Dessoky, E. M. Elsayed , On the solutions and periodic nature of some systems of rational difference equations, J. Comput. Anal. Appl., 18 (2015), 206-218
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H. El-Metwally, E. M. Elsayed, Form of solutions and periodicity for systems of difference equations, J. Comput. Anal. Appl., 15 (2013), 852-857
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H. El-Metwally, E. M. Elsayed, Qualitative behavior of some rational difference equations, J. Comput. Anal. Appl., 20 (2016), 226-236
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H. A. El-Morshedy, E. Liz , Convergence to equilibria in discrete population models, J. Difference Equ. Appl., 11 (2005), 117-131
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H. A. El-Morshedy, E. Liz, Globally attracting fixed points in higher order discrete population models, J. Math. Biol., 53 (2006), 365-384
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A. A. Elsadany, A. E. Matouk, Dynamic Cournot duopoly game with delay, J. Complex Syst., 2014 (2014), 1-7
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E. M. Elsayed, Solution and attractivity for a rational recursive sequence, Discrete Dyn. Nat. Soc., 2011 (2011), 1-17
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E. M. Elsayed , Solutions of rational difference systems of order two , Math. Comput. Modelling, 55 (2012), 378-384
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E. M. Elsayed , On the solutions and periodic nature of some systems of difference equations, Int. J. Biomath., 7 (2014), 1-26
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E. M. Elsayed , On a max type recursive sequence of order three, Miskolc Math. Notes, 17 (2016), 837-859
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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 (2011), 1026-1038
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E. M. Elsayed, A. Alghamdi, Dynamics and global stability of higher order nonlinear difference equation , J. Comput. Anal. Appl., 21 (2016), 493-503
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E. M. Elsayed, T. F. Ibrahim, Periodicity and solutions for some systems of nonlinear rational difference equations, Hacet. J. Math. Stat., 44 (2015), 1361-1390
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E. M. Elsayed, T. F. Ibrahim , Solutions and periodicity of a rational recursive sequences of order five, Bull. Malays. Math. Sci. Soc., 38 (2015), 95-112
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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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Y. Halim , Global character of systems of rational difference equations, Electron. J. Math. Anal. Appl., 3 (2015), 204-214
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S. S. Hassan, E. Chatterjee, Dynamics of the equation \(z_{n+1} = \frac{\alpha+\beta z_n}{ A+z_{n-1}}\) in the complex plane, Cogent Math., 2 (2015), 1-12
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D. Jana, E. M. Elsayed, Interplay between strong Allee effect, harvesting and hydra effect of a single population discrete-time system, Int. J. Biomath., 9 (2016), 1-25
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R. Karatas, C. Cinar, D. Simsek, On positive solutions of the difference equation \(x_{n+1} = \frac {x_{n-5}}{ 1+x_{n-2}x_{n-5}}\) , Int. J. Contemp. Math. Sci., 1 (2006), 494-500
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A. E. Matouk, A. A. Elsadany, E. Ahmed, H. N. Agiza, Dynamical behavior of fractional-order Hastings-Powell food chain model and its discretization, Commun. Nonlinear Sci. Numer. Simul., 27 (2015), 153-167
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D. Tollu, Y. Yazlik, N. Taskara, The solutions of four Riccati difference equations associated with Fibonacci numbers, Balkan J. Math., 2 (2014), 163-172
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N. Touafek, E. M. Elsayed , On a second order rational systems of difference equations, Hokkaido Math. J., 44 (2015), 29-45
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Y. Yazlik, E. M. Elsayed, N. Taskara, On the behaviour of the solutions of difference equation systems, J. Comput. Anal. Appl., 16 (2014), 932-941
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]
A quantitative approach to syndetic transitivity and topological ergodicity
A quantitative approach to syndetic transitivity and topological ergodicity
en
en
In this paper, we give new quantitative
characteristics of degrees of syndetical transitivity and
topological ergodicity for a given discrete dynamical system, which
are nonnegative real numbers and are not more than \(1\). For selfmaps
of many compact metric spaces it is proved that a given selfmap is
syndetically transitive if and only if its degree of syndetical
transitivity is \(1\), and that it is topologically ergodic if and
only if its degree of topological ergodicity is one. Moreover, there
exists a selfmap of \([0, 1]\) having all degrees positive.
4680
4686
Yu
Zhao
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
datom@189.cn
Risong
Li
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
gdoulrs@163.com
Tianxiu
Lu
Department of Mathematics
Artificial Intelligence Key Laboratory of Sichuan Province
Bridge Non-destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province
Sichuan University of Science and Engineering
People's Republic of China
People’s Republic of China
People’s Republic of China
lubeeltx@163.com
Ru
Jiang
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
jiru1995@163.com
Hongqing
Wang
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
wanghq3333@126.com
Haihua
Liang
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
lhhlucy@126.com
Sensitivity
syndetically sensitive
ergodically sensitive
multi-sensitive
cofinitely sensitive
Furstenberg families.
Article.10.pdf
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R. L. Adler, A. G. Konheim, M. H. McAndrew , Topological entropy , Trans. Amer. Math. Soc., 114 (1965), 309-319
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R. Li , A note on the three versions of distributional chaos, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 1993-1997
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R. Li , A note on shadowing with chain transitivity, Commun. Nonlinear Sci. Numer. Simulat., 17 (2012), 2815-2823
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R. Li , A note on stronger forms of sensitivity for dynamical systems, Chaos Solitons Fractals, 45 (2012), 753-758
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R. Li , The large deviations theorem and ergodic sensitivity, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 819-825
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R. Li , A note on decay of correlation implies chaos in the sense of Devaney, Appl. Math. Model., 39 (2015), 6705-6710
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R. Li, A note on chaos and the shadowing property , Int. J. Gen. Syst., 45 (2016), 675-688
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R. Li, Y. Shi , Stronger forms of sensitivity for measure-preserving maps and semiflows on probability spaces , Abstr. Appl. Anal., 2014 (2014), 1-10
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R. Li, H.-Q. Wang, Y. Zhao , Kato’s chaos in duopoly games , Chaos Solitons Fractals, 84 (2016), 69-72
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T. K. S. Moothathu, Stronger forms of sensitivity for dynamical systems, Nonlinearity, 20 (2007), 2115-2126
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L. Snoha, V. Špitalský, A quantitative approach to transitivity and mixing, Chaos Solitons Fractals, 40 (2009), 958-965
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J.-C. Xiong , Chaos in a topologically transitive system, Sci. China Ser. A, 48 (2005), 929-939
]
A modified constraint shifting homotopy method for solving general nonlinear multiobjective programming
A modified constraint shifting homotopy method for solving general nonlinear multiobjective programming
en
en
In this paper, for solving the general nonconvex multiobjective
programming with both inequality and equality constraints, a
modified constraint shifting homotopy is constructed, and the
existence and global convergence of the smooth homotopy pathway is
proven for any initial point in the almost Euclidean space under
some mild conditions. The advantage of the newly proposed method
requires that the initial point can be chosen much more
conveniently, which needs to be only in the shifted feasible set not
necessarily in the original feasible set. Meanwhile, the normal cone
condition for proving the global convergence, which is much weaker than
the existing interior method, need only be satisfied at the boundary
of the shifted feasible set but not the original constraint set.
4687
4694
Zhichuan
Zhu
School of Statistics
School of Mathematics and Statistics
Jilin University of Finance and Economics
Northeast Normal University
China
China
zhuzcnh@126.com
Yonghong
Yao
School of Mathematics and Statistics
Northeast Normal University
China
yaoyonghong@aliyun.com
Homotopy method
nonconvex programming
multiobjective programming
global convergence.
Article.11.pdf
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]
Fixed point theorems in dislocated quasi-metric spaces
Fixed point theorems in dislocated quasi-metric spaces
en
en
In this paper, we discuss the existence and uniqueness of a fixed point in a dislocated quasi-metric space. Several
fixed point theorems for distinct type of contractive conditions are presented that generalize, extend, and unify
a number of related results reported in the literature. Illustrative examples are provided.
4695
4703
Shizheng
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
College of Mathematical Sciences
Linyi University
Dezhou University
P. R. China
P. R. China
Akbar
Zada
Department of Mathematics
University of Peshawar
Pakistan
Rahim
Shah
Department of Mathematics
University of Peshawar
Pakistan
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Information Science and Engineering
Linyi University
Linyi University
P. R. China
P. R. China
litongx2007@163.com
Dislocated quasi-metric space
fixed point
contraction mapping
self-mapping
Cauchy sequence.
Article.12.pdf
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[1]
C. T. Aage, J. N. Salunke, Some results of fixed point theorem in dislocated quasi-metric spaces, Bull. Marathwada Math. Soc., 9 (2008), 1-5
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C. T. Aage, J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci. (Ruse), 2 (2008), 2941-2948
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A. Isufati , Fixed point theorems in dislocated quasi-metric space, Appl. Math. Sci. (Ruse), 4 (2010), 217-223
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K. Zoto, S. Radenović,, J. Dine, I. Vardhami , Fixed points of generalized (\(\psi,s,\alpha\))-contractive mappings in dislocated and b-dislocated metric spaces, Commun. Optim. Theory, 2017 (2017), 1-16
]
Non-self multivariate contraction mapping principle in Banach spaces
Non-self multivariate contraction mapping principle in Banach spaces
en
en
The purpose of this article
is to prove the non-self multivariate contraction mapping principle in a Banach space. The main result is the following: let \(C\) be a nonempty closed convex subset of a Banach space \((X,\|\cdot\|)\).
Let \(T: C \rightarrow X\) be a weakly inward \(N\)-variables non-self contraction mapping. Then \(T\) has a unique multivariate fixed point \(p\in C\). That is, there exists a unique element \(p \in C\) such that \(T(p,p,\cdots ,p)=p\). In order to get the non-self multivariate contraction mapping principle, the inward and weakly inward
\(N\)-variables non-self mappings are defined. In addition, the meaning
of \(N\)-variables non-self contraction mapping \(T: C \rightarrow X\) is the following:
\[
\|Tx-Ty\|\leq h \nabla (\|x_1-y_1\|, \|x_2-y_2\|,\cdots ,\|x_N-y_N\|)
\]
for all \(x=(x_1,x_2, \cdots, x_N), \ y=(y_1,y_2, \cdots, y_N)\in C^N\), where \(h \in (0,1)\) is a constant, and \(\nabla\) is an \(N\)-variables real function satisfying some suitable conditions.
The results of this article improve and extend the previous results given in the literature.
4704
4712
Yanxia
Tang
Department of Mathematics, College of Science
Hebei North University
China
sutang2016@163.com
Jinyu
Guan
Department of Mathematics, College of Science
Hebei North University
China
guanjinyu2010@163.com
Yongchun
Xu
Department of Mathematics, College of Science
Hebei North University
China
hbxuyongchun@163.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
China
tjsuyongfu@163.com
Non-self mapping
Caristi’s fixed point theorem
contraction mapping principle
multivariate fixed point
inward condition
weakly inward condition
iterative sequence.
Article.13.pdf
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[1]
R. Agarwal, D. Regan, D. Rahu , Fixed point theory for Lipschitzian-type mappings with applications, Springer, New York (2009)
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Y. Su, J.-C. Yao, Further generalized contraction mapping principle and best proximity theorem in metric spaces, Fixed Point Theory and Appl., 2015 (2015), 1-13
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F. Yan Y. Su, Q. Feng, A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl., 2012 (2012), 1-13
]
Fractional neutral stochastic differential equations driven by \(\alpha\)-stable process
Fractional neutral stochastic differential equations driven by \(\alpha\)-stable process
en
en
In this paper, we are concerned with a class of fractional neutral stochastic partial differential equations driven by \(\alpha\)-stable process. By the stochastic analysis technique, the properties of operator semigroup and combining the Banach fixed-point theorem, we prove the existence and uniqueness of the mild solutions to this kind of equations driven by \(\alpha\)-stable process. In the end, an example is given to demonstrate the theory of our work.
4713
4723
Zhi
Li
School of Information and Mathematics
Yangtze University
China
lizhi csu@126.com
Fractional neutral SDEs
\(\alpha\)-stable process
existence and uniqueness.
Article.14.pdf
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D. Applebaum, Lévy processes and stochastic calculus, Second edition, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (2009)
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P. Kalamani, D. Baleanu, S. Selvarasu, M. M. Arjunan, On existence results for impulsive fractional neutral stochastic integro-differential equations with nonlocal and state-dependent delay conditions, Adv. Difference Equ., 163 (2016), 1-36
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K.-X. Li, J.-G. Peng , Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys., 65 (2014), 941-959
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R. Sakthivel, S. Suganya, S. M. Anthoni , Approximate controllability of fractional stochastic evolution equations, Comput. Math. Appl., 63 (2012), 660-668
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Y. Zhou, F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl., 59 (2010), 1063-1077
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]
A generalized \(\theta\)-contraction and related fixed point theorems
A generalized \(\theta\)-contraction and related fixed point theorems
en
en
We introduce two types of generalized \(\theta\)-contraction mappings in complete metric spaces. For each type, we study the existence of fixed points. The obtained results in this paper generalize several existing fixed point theorems in the literature. We end this work with some open questions.
4724
4733
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
Fixed point
generalized \(\theta\)-contraction of type (I)
generalized \(\theta\)-contraction of type (II)
partial order
\(\theta\)-cyclic contraction.
Article.15.pdf
[
[1]
S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fundam. Math., 3 (1922), 133-181
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M. Berinde, V. Berinde , On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl., 326 (2007), 772-782
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##[4]
A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37
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M. Cherichi, B. Samet, Fixed point theorems on ordered gauge spaces with applications to nonlinear integral equations, Fixed Point Theory Appl., 2012 (2012), 1-19
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L. Ćirić, Multi-valued nonlinear contraction mappings, Nonlinear Anal., 71 (2009), 2716-2723
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M. Jleli, E. Karapinar, B. Samet , Further generalizations of the Banach contraction principle, J. Inequal Appl., 2014 (2014), 1-9
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M. Jleli, B. Samet , A new generalization of the Banach contraction principle, J. Ineq. Appl., 2014 (2014), 1-8
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E. Karapinar, Fixed points results for \(\alpha\) admissible mapping of integral type on generalized metric spaces, Abstr. Appl. Anal., 2015 (2015), 1-11
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W. A. Kirk, N. Shahzad, Generalized metrics and Caristis theorem, Fixed Point Theory Appl., 2013 (2013), 1-9
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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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D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-6
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]
Uniqueness result for the cantilever beam equation with fully nonlinear term
Uniqueness result for the cantilever beam equation with fully nonlinear term
en
en
In this paper, the uniqueness of solution for the cantilever beam equation with fully nonlinear term is obtained by using the method of order reduction and the theory of linear operators. A simple comparison is given to show that the obtained results provide the same results with weaker conditions.
4734
4740
Yumei
Zou
Department of Statistics and Finance
Shandong University of Science and Technology
P. R. China
sdzouym@126.com
Yujun
Cui
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology
Shandong University of Science and Technology
P. R. China
cyj720201@163.com
Fully fourth-order boundary value problem
uniqueness theorem
order reduction
Banach’s contraction mapping principle.
Article.16.pdf
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[1]
A. R. Aftabizadeh , Existence and uniqueness theorems for fourth-order boundary value problems , J. Math. Anal. Appl., 116 (1986), 415-426
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R. P. Agarwal, D. O’Regan , Twin solutions to singular boundary value problems, Proc. Amer. Math. Soc., 128 (2000), 2085-2094
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R. P. Agarwal, D. O’Regan, V. Lakshmikantham , Singular (p, n - p) focal and (n, p) higher order boundary value problems, Nonlinear Anal., 42 (2000), 215-228
##[4]
Y.-J. Cui, Uniqueness of solution for boundary value problems for fractional differential equations, Appl. Math. Lett., 15 (2016), 48-54
##[5]
Y.-J. Cui, Y.-M. Zou , An existence and uniqueness theorem for a second order nonlinear system with coupled integral boundary value conditions , Appl. Math. Comput., 255 (2015), 438-444
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L. Guo, L. Liu, Y.-H. Wu , Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions, Boundary Value Problems, 2016 (2016), 1-20
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G. Infante, P. Pietramala, A cantilever equation with nonlinear boundary conditions, Electron. J. Qual. Theory Differ. Equ., 2009 (2009), 1-14
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M. A. Krasnosel'skiĭ, Positive Solutions of Operator Equations, P. Noordhoff, Groningen, Netherlands (1964)
##[10]
Y.-X. Li, Existence of positive solutions for the cantilever beam equations with fully nonlinear terms, Nonlinear Anal. Real World Appl., 27 (2016), 221-237
##[11]
F. Minhós, T. Gyulov, A. I. Santos, Lower and upper solutions for a fully nonlinear beam equation, Nonlinear Anal., 71 (2009), 281-292
##[12]
Q.-L. Yao, Monotonically iterative method of nonlinear cantilever beam equations, Appl. Math. Comput., 205 (2008), 432-437
##[13]
Q.-L. Yao , Local existence of multiple positive solutions to a singular cantilever beam equation, J. Math. Anal. Appl., 363 (2010), 138-154
##[14]
Y. Zou, G.-P. He, On the uniqueness of solutions for a class of fractional differential equations, Appl. Math. Lett., 74 (2017), 68-73
]
Multivariate contraction mapping principle in Menger probabilistic metric spaces
Multivariate contraction mapping principle in Menger probabilistic metric spaces
en
en
The purpose of this paper is to prove the multivariate contraction mapping principle of \(N\)-variables mappings in Menger probabilistic metric spaces. In order to get the multivariate contraction mapping principle, the product spaces of Menger probabilistic metric spaces are subtly defined which is used as an important method for the expected results. Meanwhile, the relative iterative algorithm of the multivariate fixed point is established. The results of this paper improve and extend the contraction mapping principle of single variable mappings in the probabilistic metric spaces.
4741
4750
Jinyu
Guan
Department of Mathematics, College of Science
Hebei North University
China
guanjinyu2010@163.com
Yanxia
Tang
Department of Mathematics, College of Science
Hebei North University
China
sutang2016@163.com
Yongchun
Xu
Department of Mathematics, College of Science
Hebei North University
China
hbxuyongchun@163.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
China
tjsuyongfu@163.com
Contraction mapping principle
probabilistic metric spaces
product spaces
multivariate fixed point.
Article.17.pdf
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]
Strong convergence of a modified viscosity iteration for common zeros of a finite family of accretive mappings
Strong convergence of a modified viscosity iteration for common zeros of a finite family of accretive mappings
en
en
A new modified
iterative scheme \(\{x_n\}\) is given for the viscosity approximating a common zero of a finite family of accretive mappings \(\{A_{i}\}\)
in reflexive Banach spaces with a weakly
continuous duality mapping \(J\) in the present paper. Under certain conditions, we prove the strong convergence
of the sequence \(\{x_n\}\). The results here extend and improve the corresponding recent results of some other authors.
4751
4759
Yuanheng
Wang
Department of Mathematics
Zhejiang Normal University
China
yhwang@zjnu.cn
Yan
Li
Department of Basic Science
Nanyang Polytechnic Institute
China
lirongfu703@sina.com
Chanjuan
Pan
Department of Mathematics
Zhejiang Normal University
China
cjpanzjnu@163.com
Viscosity approximation method
accretive mapping
common zero
strong convergence
reflexive Banach space.
Article.18.pdf
[
[1]
L. C. Ceng, A. R. Khan, Q. H. Ansari, J. C. Yao, Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces, Nonlinear Anal., 70 (2009), 1830-1840
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R. D. Chen, Y. J. Liu, X. L. Shen, Iterative approximation of a zero of accretive operator in Banach space, Nonlinear Anal., 71 (2009), 346-350
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R. D. Chen, Z. C. Zhu, Viscosity approximation fixed point for nonexpansive and m-accretive operators, Fixed Point Theory Appl., 2006 (2006), 1-10
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Y. H. Wang, S. Chebbi, H. K. Xu , Weak convergence of an iterative format for finding common zeros of two accretive operators in Banach spaces, J. Nonlinear Convex Anal., 16 (2015), 1937-1947
##[12]
Y. H. Wang, Y. H. Xia, Strong convergence for asymptotically pseudocontractions with the demiclosedness principle in Banach spaces, Fixed Point Theory Appl., 2012 (2012), 1-8
##[13]
H. K. Xu , Iterative algorithms for nonlinear operator, J. London Math. Soc., 66 (2002), 240-256
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H. K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
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H. K. Xu , Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl., 314 (2006), 631-643
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H. Zegeye, N.Shahzad , Strong convergence theorems for a common zero of a finite family of m-accretive mapping, Nonlinear Anal., 66 (2007), 1161-1169
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Q. Yuan, S. Lv , Strong convergence of a parallel iterative algorithm in a reflexive banach space, Fixed Point Theory Appl., 2014 (2014), 1-9
]
On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions
On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions
en
en
In this manuscript, using Schaefer's fixed point theorem, we derive some sufficient conditions for the existence of solutions to a class of fractional differential equations (FDEs). The proposed class is devoted to the impulsive FDEs with nonlinear integral boundary condition. Further, using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss various kinds of Ulam-Hyers stability. Finally to illustrate the established results, we provide an example.
4760
4775
Arshad
Ali
Department of Mathematics
University of Malakand
Pakistan
arshad.swatpk@gmail.com
Faranak
Rabiei
Department of Mathematics, Faculty of Science
Institute For Mathematical Research
Universiti Putra Malaysia
Universiti Putra Malaysia
Malaysia
Malaysia
faranak_rabiei@upm.edu.my
Kamal
Shah
Department of Mathematics
University of Malakand
Pakistan
kamalshah408@gmail.com
Caputo fractional derivative
integral boundary conditions
impulsive condition
fixed point theorem
Ulam stability.
Article.19.pdf
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S. András, J. J. Kolumbán, On the Ulam-Hyers stability of first order differential systems with nonlocal initial conditions, Nonlinear Anal., 82 (2013), 1-11
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]
Dynamics of a stochastic delay competition model with imprecise parameters
Dynamics of a stochastic delay competition model with imprecise parameters
en
en
This paper is concerned with a two-species delay stochastic competition model with imprecise parameters. We first obtain the thresholds between persistence and extinction for each species. Then we establish sharp sufficient criteria for the existence of a unique ergodic stationary distribution of the model. The effects of imprecise parameters on the persistence, extinction and existence of the stationary distribution are revealed. Finally, we work out some numerical simulations to illustrate the theoretical results.
4776
4788
Xin
He
School of Mathematical Science
Huaiyin Normal University
P. R. China
Meng
Liu
School of Mathematical Science
School of Mathematics and Statistics
Huaiyin Normal University
Northeast Normal University
P. R. China
P. R. China
liumeng0557@163.com
Competition system
stochastic perturbations
imprecise parameters
time delay.
Article.20.pdf
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]
Best proximity point theorems for generalized \(\alpha\)-proximal contractions in Banach spaces
Best proximity point theorems for generalized \(\alpha\)-proximal contractions in Banach spaces
en
en
In this paper, we obtain the best proximity point theorem for \(\alpha\)-proximal contraction of the first and second kinds in Banach spaces by using fixed point theorems. Also, we mention an example for justification of our results.
4789
4798
Somayya
Komal
Department of Mathematics, Faculty of Science
King Mongkut's University of Technology Thonburi (KMUTT)
Thailand
somayya.komal@mail.kmutt.ac.th
Poom
Kumam
Department of Mathematics, Faculty of Science
KMUTT-Fixed Point Theory and ApplicationsResearch Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science
Department of Medical Research, China Medical University Hospital
King Mongkut’s University of Technology Thonburi (KMUTT)
King Mongkut’s University of Technology Thonburi (KMUTT)
China Medical University
Thailand
Thailand
Taiwan
poom.kum@kmutt.ac.th
Phatiphat
Thounthong
Renewable Energy Research Centre
Department of Teacher Training in Electrical Engineering, Faculty of Technical Education
King Mongkut’s University of Technology North Bangkok (KMUTNB),
King Mongkuts University of Technology North Bangkok (KMUTNB)
Thailand
Thailand
Kanokwan
Sitthithakerngkiet
Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok (KMUTNB)
Thailand
kanokwan.s@sci.kmutnb.ac.th
Best proximity point
generalized \(\alpha\)-proximal contraction of the first and second kinds
approximatively compactness.
Article.21.pdf
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P. Ardsalee, S. Saejung, Best proximity point theorems via fixed point theorems for multivalued mappings, Fixed Point Theory Appl., 2016 (2016), 1-11
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A. Fernández-León , Best proximity points for proximal contractions, J. Nonlinear Convex Anal., 15 (2014), 313-324
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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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M. Jleli, B. Samet, Remarks on the paper: Best proximity point theorems: an exploration of a common solution to approximation and optimization problems, Appl. Math. Comput., 228 (2014), 366-370
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]
Iterative algorithm for a common fixed point of two mono-pseudocontractive mappings in Banach spaces
Iterative algorithm for a common fixed point of two mono-pseudocontractive mappings in Banach spaces
en
en
In this paper, we introduce an iterative process which converges
strongly to a common fixed point of two mono-pseudocon-tractive
mappings in Banach spaces.
Our theorems complement the results that have been proved
for the class of pseudocontractive mappings in Banach spaces.
4799
4811
Naseer
Shahzad
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nshahzad@kau.edu.sa
Habtu
Zegeye
Department of Mathematics
Botswana International University of Science and Technology
Botswana
habtuzh@yahoo.com
Monotone mapping
pseudocontractive mapping
mono-pseudocontractive mapping
strong convergence.
Article.22.pdf
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]
A projection-type method for generalized variational inequalities with dual solutions
A projection-type method for generalized variational inequalities with dual solutions
en
en
In this paper, a new projection-type method for generalized variational inequalities is introduced in Euclidean spaces. Under the assumption that the dual variational inequality has a solution, we show that the proposed method is well-defined and prove that the sequence generated by the proposed method is convergent to a solution, where the condition is strictly weaker than the pseudomonotonicity of the mapping used by some authors. We provide an example to support our results. Compared with the recent works of Li and He [F.-L. Li, Y.-R. He, J. Comput. Appl. Math., \({\bf 228}\) (2009), 212--218], and Fang and He [C.-J. Fang, Y.-R. He, Appl. Math. Comput., \({\bf 217}\) (2011), 9543--9551], condition (A3) is removed. Moreover, the results presented in this paper also generalize and improve some
known results given in other literature.
4812
4821
Ming
Zhu
School of Science
Guangxi University for Nationalities
P. R. China
Guo-Ji
Tang
School of Science
Guangxi University for Nationalities
P. R. China
guojvtang@126.com;guojvtang@hotmail.com
Projection method
generalized variational inequality
dual variational inequality.
Article.23.pdf
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]
An accelerated Newton method of high-order convergence for solving a class of weakly nonlinear complementarity problems
An accelerated Newton method of high-order convergence for solving a class of weakly nonlinear complementarity problems
en
en
In this paper, by extending the classical Newton method, we investigate an accelerated Newton iteration method (ANIM) with high-order convergence for solving a class of weakly nonlinear complementarity problems which arise from the discretization of free boundary problems. Theoretically, the performance of high-order convergence is analyzed in details. Some numerical experiments demonstrate the efficiency of the presented method.
4822
4833
Ya-Jun
Xie
College of Mathematics and Informatics, Fujian Key Laboratory of Mathematical Analysis and Applications
Department of Mathematics and Physics
Fujian Normal University
Fujian Jiangxia University
P. R. China
P. R. China
Na
Huang
College of Mathematics and Informatics, Fujian Key Laboratory of Mathematical Analysis and Applications
Academy of Mathematics and Systems Science
Fujian Normal University
Chinese Academy of Sciences
P. R. China
P. R. China
Chang-Feng
Ma
College of Mathematics and Informatics, Fujian Key Laboratory of Mathematical Analysis and Applications
Fujian Normal University
P. R. China
macf@fjnu.edu.cn
Weakly nonlinear complementarity problems
high-order convergence
the modulus-based nonlinear function
convergence analysis
numerical experience.
Article.24.pdf
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Global and local behavior of a class of \(\xi^{(s)}\)-QSO
Global and local behavior of a class of \(\xi^{(s)}\)-QSO
en
en
A quadratic stochastic operator (QSO) describes the time evolution of different species in biology. The main problem with regard to a nonlinear operator is to study its behavior. This has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly.
This paper investigates the global behavior of an operator taken from \(\xi^{(s)}\)-QSO when the parameter \(a=\frac{1}{2}\). Moreover, we study the local behavior of this operator at each value of \(a,\) where \(0< a < 1\).
4834
4845
Abdelwahab
Alsarayreh
Institute of Engineering Mathematics
University Malaysia
Malaysia
abdalwahb.saraereh@gmail.com
Izzat
Qaralleh
Department of mathematics, Faculty of Science
Tafila Technical University
Jordan
izzat_math@yahoo.com
Muhammad Zaini
Ahmad
Institute of Engineering Mathematics
University Malaysia
Malaysia
mzaini@unimap.edu.my
Basma
Al-Shutnawi
Department of mathematics, Faculty of Science
Tafila Technical University
Jordan
salmashut@yahoo.com
Saba
Al-Kaseasbeh
Department of mathematics, Faculty of Science
Tafila Technical University
Jordan
skasabeh@ttu.edu.jo
Quadratic stochastic operator
local behavior
global behavior.
Article.25.pdf
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]
Endpoint estimates for commutators of mutilinear square function satisfying some integrable condition
Endpoint estimates for commutators of mutilinear square function satisfying some integrable condition
en
en
In this paper, the \((L^{p_1}\times\cdots\times L^{p_m},L^q)\)-estimate for the commutator \(T_{\Pi b}\) generalized by multilinear square function \(T\)
and Lipschitz function \(\vec{b}\) is established for \(\frac{1}{q}=\sum_{j=1}^m\frac{1}{p_i}-\frac{\beta}n,~ p_i>p_0\ge1\).
Meanwhile, we also establish \((L^{p_1}\times\cdots\times L^{p_m}, \dot{\Lambda}_{\beta-\frac{n}p} )\)-boundedness
and \((L^{\frac{n}{\beta_1}}\times\cdots\times L^{\frac{n}{\beta_m}},BMO)\)-estimates for the commutator \(T_{\Pi b}\). Finally, the \((L^{p_1}\times\cdots\times L^{p_m}, \dot{F}_{p}^{\beta,\infty})\)-boundedness is obtained, too.
4846
4865
Dongxiang
Chen
Department of Mathematic and information Science
Jiangxi Normal University
China
chendx020@aliyun.com
Anzhi
Huang
Department of Mathematic and information Science
Jiangxi Normal University
China
18779100971@163.com
Multilinear square function
iterated commutator
Lipschitz space
Triebel-Lizorkin space.
Article.26.pdf
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Fixed point results for multivalued mappings in \({\mathbf G}_{b}\)-cone metric spaces
Fixed point results for multivalued mappings in \({\mathbf G}_{b}\)-cone metric spaces
en
en
The aim of this paper is to introduce the
notion of generalized Hausdorff distance function on \(G_{b}\)-cone metric
spaces and exploit it to study some fixed point results in the setting of \(G_{b}\)-cone metric spaces without the assumption of normality. These results
improve and generalize some important known results. Some illustrative
examples are also furnished to highlight the realized improvements.
4866
4875
Abdullah Eqal
Al-Mazrooei
Department of Mathematics
University of Jeddah
Saudi Arabia
aealmazrooei@uj.edu.sa
Jamshaid
Ahmad
Department of Mathematics
University of Jeddah
Saudi Arabia
jkhan@uj.edu.sa;jamshaid_jasim@yahoo.com
Non normal cone
fixed points
\(G_{b}\)-cone metric space
Article.27.pdf
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[1]
J. Ahmad, A. S. Al-Rawashdeh, A. Azam, Fixed point results for \(\{\alpha,\xi\}\)-expansive locally contractive mappings, J. Inequal. Appl., 2014 (2014), 1-10
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Stability control of fractional chaotic systems based on a simple Lyapunov function
Stability control of fractional chaotic systems based on a simple Lyapunov function
en
en
In this paper the stabilization of fractional-order chaotic systems and a new property of fractional derivatives are studied. Then we propose a new fractional-order extension of Lyapunov direct method and a control method based on a simple Lyapunov candidate function. The proposed control method can be applied to the stabilization of fractional-order chaotic and hyperchaotic systems. This control method is simple, universal, and theoretically rigorous. Numerical simulations are given for three fractional-order chaotic (or hyperchaotic) systems to verify the effectiveness and the universality of the proposed control method.
4876
4889
Tianzeng
Li
School of Mathematics and Statistics, Artificial Intelligence Key Laboratory of Sichuan Province
Sichuan university of Science and Engineering
China
litianzeng27@163.com
Yu
Wang
School of Mathematics and Statistics, Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things
Sichuan university of Science and Engineering
China
wangyu_813@163.com
Hongmei
Li
School of Economic and Management
Northwest University
China
hmli@nwu.edu.cn
Lyapunov function
fractional-order
stabilization
Article.28.pdf
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[1]
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]
A generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces
A generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces
en
en
A generalized forward-backward method
for solving split equality quasi inclusion problems of accretive
operators in Banach spaces is studied. Some strong convergence theorems for the sequences generalized by the algorithm to a solution of quasi inclusion problems of accretive
operators are proved under certain assumptions. The results presented in this paper are new which extend and improve the corresponding results
announced in the recent literatures. At the end of the paper
some applications to monotone variational inequalities, convex minimization problem, and convexly constrained linear inverse problem are presented.
4890
4900
Shih-Sen
Chang
Center for General Education
College of Statistics and Mathematics
China Medical University
Yunnan University of Finance and Economics
Taiwan
China
changss2013@163.com
Ching-Feng
Wen
Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization
Department of Medical Research
Kaohsiung Medical University
Kaohsiung Medical University Hospital
Taiwan
Taiwan
cfwen@kmu.edu.tw
Jen-Chih
Yao
Center for General Education
China Medical University
Taiwan
yaojc@mail.cmu.edu.tw
Jing-Qiang
Zhang
College of Statistics and Mathematics
Yunnan University of Finance and Economics
China
geminitiger@163.com
Generalized forward-backward method
accretive operator
\(m\)-accretive operator
maximal monotone operator
split equality quasi inclusion problem
Article.29.pdf
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C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
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S.-S. Chang, L. Wang, L.-J. Qin, Z.-L. Ma , Strongly convergent iterative methods for split equality variational inclusion problems in Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 36 (2016), 1641-1650
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On cycle inequalities for convex-star bodies
On cycle inequalities for convex-star bodies
en
en
In this paper, we establish new cycle inequalities
for convex-star bodies, which are joint improvements of the cycle
inequality for convex bodies and the dual cycle inequality for
star bodies.
4901
4907
Chang-Jian
Zhao
Department of Mathematics
China Jiliang University
P. R. China
chjzhao@163.com;chjzhao@aliyun.com
Wing-Sum
Cheung
Department of Mathematics
China Jiliang University
P. R. China
wscheung@hku.hk
Convex body
star body
mixed volume
dual mixed volume
the cycle inequality
the dual cycle inequality
Article.30.pdf
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Y. D. Burago, V. A. Zalgaller, Geometric inequalities, Translated from the Russian by A. B. Sosinskiĭ, Grundlehren der MathematischenWissenschaften [Fundamental Principles of Mathematical Sciences], Springer Series in Soviet Mathematics, Springer-Verlag, Berlin (1988)
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]
A pinching theorem for statistical manifolds with Casorati curvatures
A pinching theorem for statistical manifolds with Casorati curvatures
en
en
With a pair of conjugate connections \(\overline{\nabla}\) and \(\overline{\nabla}^*\), we derive optimal Casorati inequalities with the normalized scalar curvature on submanifolds of a statistical manifold of constant curvature.
4908
4914
Chul Woo
Lee
Department of Mathematics
Kyungpook National University
South Korea
mathisu@knu.ac.kr
Dae Won
Yoon
Department of Mathematics Education
Gyeongsang National University and RINS
South Korea
dwyoon@gnu.ac.kr
Jae Won
Lee
Department of Mathematics Education
Gyeongsang National University and RINS
South Korea
leejaew@gnu.ac.kr
Statistical manifolds
dual connection
Casorati curvature
\(\delta\)-Casorati curvature
normalized scalar curvature
Article.31.pdf
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J. W. Lee, C. W. Lee, D. W. Yoon, Inequalities for generalized \(\delta\)-Casorati curvatures of submanifolds in real space forms endowed with a semi-symmetric metric connection, Rev. Un. Mat. Argentina, 57 (2016), 53-62
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]
Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor
Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor
en
en
This paper investigates matrix Fourier multiwavelet frames
multipliers with dilation factor \(a\). First, the definition of
matrix Fourier multiwavelet frame multiplier was proposed, which is
\(N_1\times N\) matrices with \(L^\infty\) function entries, and maps
Parseval multiwavelet frames of length \(N\) to Parseval multiwavelet
frames of length \(N_1\). Then, two sufficient conditions of matrix
Fourier multiwavelet frame multiplier were given, and two necessary
conditions of matrix Fourier multiwavelet frame multiplier were
characterized by means of frame wavelet sets. Finally, several
numerical examples were constructed. As Fourier wavelet frames
multiplier, matrix Fourier multipliers can be used to derive new
Parseval multiwavelet frames and can help us better understand the
basic of frame theory.
4915
4929
Fengjuan
Zhu
School of Mathematics and Information Science
North Minzu University
China
xiao jinlin@163.com
Yongdong
Huang
School of Mathematics and Information Science
North Minzu University
China
nxhyd74@126.com
Shengnan
Shi
School of Mathematics and Information Science
North Minzu University
China
977998177@qq.com
Xiao
Tan
School of Mathematics and Information Science
North Minzu University
China
13649507784@163.com
Juan
Zhao
School of Mathematics and Information Science
North Minzu University
China
1334801264@qq.com
Parseval frames multiwavelet
Fourier multipliers
matrix Fourier multiwavelet frames multipliers
frame wavelet set
Article.32.pdf
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[1]
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]
Infinitely many small energy solutions for fractional coupled Schrodinger system with critical growth
Infinitely many small energy solutions for fractional coupled Schrodinger system with critical growth
en
en
In this paper, we investigate the small energy solutions for a coupled fractional Schrödinger system with critical growth. The existence criteria of infinitely many small energy solutions are established without Ambrosetti-Rabinowitz (A-R) condition by variant fountain theorem. Our main results are completely new and complement the previously known studies.keywords
4930
4939
Peiluan
Li
School of Mathematics and Statistics
Henan University of Science and Technology
China
lpllpl_lpl@163.com
Yuan
Yuan
Department of Mathematics and Statistics
Memorial University of Newfoundland
Canada
yyuan@mun.ca
Yuanxian
Hui
School of Mathematics and Statistics
Puer University
China
949014655@qq.com
Coupled fractional Schr̈odinger system
small energy solutions
critical growth
variant fountain theorem
Article.33.pdf
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W. M. Abd-Elhameed, Y. H. Youssri, Spectral solutions for fractional differential equations via a novel Lucas operational matrix of fractional derivatives , Rom. J. Phys., 61 (2016), 795-813
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##[3]
A. Agila, D. Baleanu, R. Eid, B. Irfanoglu, Applications of the extended fractional Euler-Lagrange equations model to freely oscillating dynamical systems, Rom. J. Phys., 61 (2016), 350-359
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P. Álvarez-Caudevilla, E. Colorado, V. A. Galaktionov, Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations, Nonlinear Anal. Real World Appl., 23 (2015), 78-93
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]
Multi-sensitivity, syndetical sensitivity and the asymptotic average- shadowing property for continuous semi-flows
Multi-sensitivity, syndetical sensitivity and the asymptotic average- shadowing property for continuous semi-flows
en
en
In this paper, for a continuous
semi-flow \(\theta\) on a compact metric space \(E\) with the asymptotic
average-shadowing property (AASP), we show that if the almost
periodic points of \(\theta\) are dense in \(E\) then \(\theta\) is
multi-sensitive and syndetically sensitive. Also, we show that if
\(\theta\) is a Lyapunov stable semi-flow with the AASP, then the
space \(E\) is trivial. Consequently, a Lyapunov stable semi-flow with
the AASP is minimal. Furthermore, we prove that for a syndetically
transitive continuous semi-flow on a compact metric space,
sensitivity is equivalent to syndetical sensitivity. As an
application, we show that for a continuous semi-flow \(\theta\) on a
compact metric space \(E\) with the AASP, if the almost periodic
points of \(\varphi\) are dense in \(E\) then \(\theta\) is syndetically
sensitive. {Moreover, we prove that for any continuous semi-flow \(\theta\) on a compact metric space, it has
the AASP if and only if so does its inverse limit \((\widetilde{E},
\widetilde{\theta})\), and if only if so does its lifting continuous semi-flow
\((\widehat{E}, \widehat{\theta})\). Also, an example which contains two numerical experiments is given. Our results extend some corresponding and existing ones.
4940
4953
Risong
Li
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
gdoulrs@163.com
Tianxiu
Lu
Department of Mathematics
Artificial Intelligence Key Laboratory of Sichuan Province
Bridge Non-destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province
Sichuan University of Science and Engineering
People's Republic of China
People’s Republic of China
People’s Republic of China
lubeeltx@163.com
Yu
Zhao
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
datom@189.cn
Hongqing
Wang
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
wanghq3333@126.com
Haihua
Liang
School of Mathematic and Computer Science
Guangdong Ocean University
People's Republic of China
lhhlucy@126.com
The asymptotic average-shadowing property
strong ergodicity
minimal point
multi-sensitivity
syndetical sensitivity
Lyapunov stable
Article.34.pdf
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L.-L. Huang, G.-C. Wu, M. M. Rashidi, W.-H. Luo, Chaos analysis of the nonlinear Duffing oscillators based on the new Adomian polynomials, J. Nonlinear Sci. Appl., 9 (2016), 1877-1881
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]
On subclass of meromorphic multivalent functions associated with Liu-Srivastava operator
On subclass of meromorphic multivalent functions associated with Liu-Srivastava operator
en
en
In the present paper, we introduce a new subclass related to meromorphically
\(p\)-valent reciprocal starlike functions associated with the Liu-Srivastava
operator. Some sufficient conditions for functions belonging to this class
are derived. The results presented here improve and generalize some known
results.
4954
4965
Saqib
Hussain
COMSATS Institute of Information Technology
Pakistan
saqib_math@yahoo.com
Jamila
Bibi
COMSATS Institute of Information Technology
Pakistan
syyedajameela@gmail.com
Mohsan
Raza
Department of Mathematics
Government College University
Pakistan
mohsan976@yahoo.com
Maslina
Darus
School of Mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
maslina@ukm.edu.my
Meromorphic functions
convolution
linear operator
Article.35.pdf
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[1]
N. E. Cho, I. H. Kim, Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 187 (2007), 115-121
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##[3]
J. Dziok, H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103 (1999), 1-13
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]
On quasi-linear equation problems involving critical and singular nonlinearities
On quasi-linear equation problems involving critical and singular nonlinearities
en
en
We consider the singular boundary value problem
\[ \left\{\begin{array}{l}
-\text{div}(|x|^{-ap}|\nabla u|^{p-2}\nabla u)=h(x)\frac{u^{-\gamma}}{|x|^{b(1-\gamma)}}+\mu \frac{u^{p^*-1}}{|x|^{bp^*}} \ \ \ \text{in} \ \Omega\backslash\{0\}, \cr u>0\ \ \ \ \ \text{in}\ \Omega\backslash\{0\}, \cr u=0\ \ \ \ \ \text{on} \ \partial\Omega, \end{array}\right.
\]
where \(\Omega\subset \mathbb{R}^N(N\geq 3)\) is a bounded
domain such that \(0\in \Omega\),
\(0<\gamma<1\), \(0\leq a<\frac{N-p}{p}\), \(a\leq b<a+1\), \(p^* :=p^* (a,b)=\frac{Np}{N-(1+a-b)p}\), and
\(h(x)\) is a given function.
Based on different assumptions, using variational methods and Ekeland's principle, we admit that this problem possesses two positive solutions.
keywords
4966
4982
Yanbin
Sang
Department of Mathematics, School of Science
North University of China
China
syb6662004@163.com
Xiaorong
Luo
Department of Mathematics, School of Science
North University of China
China
993237546@qq.com
Critical exponent
\(p\)-Laplacian operator
extremal value
singular nonlinearity
Article.36.pdf
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]
Positive solutions for singular higher-order semipositone fractional differential equations with conjugate type integral conditions
Positive solutions for singular higher-order semipositone fractional differential equations with conjugate type integral conditions
en
en
In this article, height functions on different bounded sets of the nonlinear term and their integrations are considered to obtain the existence of positive solutions for a class of semipositone higher-order fractional differential equations with nonlocal conjugate type integral conditions. The singularities of the nonlinearity are related to both the time and the space variables.
4983
5001
Qiuyan
Zhong
Center for Information Technology
Jining Medical University
P. R. China
zhqy197308@163.com
Xingqiu
Zhang
School of Medical Information Engineering
Jining Medical University
P. R. China
zhxq197508@163.com
Zhuyan
Shao
School of Medical Information Engineering
Jining Medical University
P. R. China
317096018@qq.com
Fractional differential equations
conjugate type integral conditions
positive solution
semipositone
singularity
Article.37.pdf
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Q. Sun, Y.-M. Cui, Solvability of (k, n - k) conjugate boundary value problems with integral boundary conditions at resonance, J. Funct. Spaces, 2016 (2016), 1-7
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Y.-Q. Wang, L.-S. Liu, Y.-H. Wu, Positive solutions for a nonlocal fractional differential equation, Nonlinear Anal., 74 (2011), 3599-3605
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X.-Q. Zhang , Positive solutions for a class of singular fractional differential equation with infinite-point boundary value conditions , Appl. Math. Lett., 39 (2015), 22-27
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X.-Q. Zhang , Positive solutions for singular higher-order fractional differential equations with nonlocal conditions, J. Appl. Math. Comput., 49 (2015), 69-89
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X.-U. Zhang, L.-S. Liu, Y.-H. 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
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X.-U. Zhang, L.-S. Liu, Y.-H. Wu, B. Wiwatanapataphee, The spectral analysis for a singular fractional differential equation with a signed measure, Appl. Math. Comput., 257 (2015), 252-263
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X.-Q. Zhang, L. Wang, Q. Sun, Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter, Appl. Math. Comput., 226 (2014), 708-718
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]
Commutators of multilinear Calderón–Zygmund operators with Dini type kernels on some function spaces
Commutators of multilinear Calderón–Zygmund operators with Dini type kernels on some function spaces
en
en
In this paper, we establish some new boundedness for commutators of multilinear Calderón-Zygmund operators with kernels of type \(\omega\) from product of Lebesgue spaces into
Lebesgue spaces, Lipschitz spaces, and Triebel-Lizorkin spaces, which extend some previous results.
5002
5019
Jie
Sun
Department of Mathematics
Mudanjiang Normal University
P. R. China
sj800816@163.com
Pu
Zhang
Department of Mathematics
Mudanjiang Normal University
P. R. China
puzhang@sohu.com
Calderón-Zygmund operator
commutator
Lipschitz space
Triebel-Lizorkin space
Article.38.pdf
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S. Chanillo, A note on commutators, Indiana Univ. Math. J., 31 (1982), 7-16
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]
Curves and surfaces of spacelike curves according to Bishop frame and their singularities
Curves and surfaces of spacelike curves according to Bishop frame and their singularities
en
en
Legendrian dualities between pseudo-spherical
images of spacelike curves in Minkowski \(3\)-space are investigated by using the theory of Legendrian duality.
Moreover, the singularities of parallel lightcone developables, dual surface, Bishop pseudo-spherical
Darboux images and Bishop pseudo-spherical images, which are generated by spacelike curves, are classified from the viewpoints of wave fronts and caustics, and we also give some more detail descriptions on the conditions of those singularities.
Finally, some properties of parallel slant helix are given.
5020
5037
Haiming
Liu
School of Mathematics
Mudanjiang Normal University
P. R. China
liuhm468@nenu.edu.cn
Jiajing
Miao
School of Mathematics
Mudanjiang Normal University
P. R. China
jiajing0407@126.com
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Spacelike curves
Minkowski \(3\)-space
Bishop frame
Legendrian dualities
Article.39.pdf
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V. I. Arnol’d , Singularities of Caustics and Wave Fronts, Kluwer Academic Publishers, Dordrecht (1990)
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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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L. Kula, N. Ekmekçi, Y. Yayli, K. Ilarslan, Characterizations of slant helices in Euclidean 3-space, Turkish J. Math., 34 (2010), 261-274
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L. Kula, Y. Yayli, On slant helix and its spherical indicatrix, Appl. Math. Comput., 169 (2005), 600-607
##[15]
H. Liu, D. Pei, Cusps of Bishop spherical indicatrixes and their visualizations, Math. Prob. Eng., 2013 (2013), 1-11
##[16]
H. Liu, D. Pei, Singularities of a space curve according to the relatively parallel adapted frame and its visualization, Math. Prob. Eng., 2013 (2013), 1-12
##[17]
H. Liu, D. Pei , Legendrian dualities between spherical indicatrixes of curves and surfaces according to Bishop frame, J. Nonlinear Sci. Appl., 9 (2016), 2875-2887
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M. Özdemir, A. A. Ergin, Parallel frames of non-lightlike curves, Missouri J. Math. Sci., 20 (2008), 127-137
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D. Ünal, I. Kisi, M. Tosun, Spinor Bishop equations of curves in Euclidean 3-space, Adv. Appl. Clifford Algebras, 23 (2013), 757-765
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S. Yılmaz, Bishop spherical images of a spacelike curve in Minkowski 3-space, Int. J. Phys. Sci., 5 (2010), 898-905
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S. Yılmaz, E. Özyılmaz, M. Turgut , New spherical indicatrix and their characterizations, An. Şt. Ovidius Constanţa , 18 (2010), 337-354
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S. Yılmaz, 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
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Proximal ADMM with larger step size for two-block separable convex programming and its application to the correlation matrices calibrating problems
Proximal ADMM with larger step size for two-block separable convex programming and its application to the correlation matrices calibrating problems
en
en
The alternating direction method of multipliers (ADMM) is a benchmark for solving two-block separable convex programming. However, as other first-order iteration methods, the ADMM also suffers from low convergence. In this paper, to accelerate the convergence of {the} ADMM, the restriction region of the Fortin and Glowinski's constant \(\gamma\) in the ADMM is relaxed from \(\Big(0,\frac{1+\sqrt{5}}{2}\Big)\) to \((0,+\infty)\), thus we get a proximal ADMM with larger step size. By proving some properties of the method, we show its global
convergence under mild conditions. Finally, some numerical experiments on the correlation matrices calibrating problems are given to demonstrate the efficiency and the performance of the new method.
5038
5051
Hongchun
Sun
School of Sciences
Linyi University
P. R. China
sunhc68@126.com
Min
Sun
School of Mathematics and Statistics
School of Management
Zaozhuang University
Qufu Normal University
P. R. China
P. R. China
ziyouxiaodou@163.com
Yiju
Wang
School of Management
Qufu Normal University
P. R. China
yiju-wang@163.com
Alternating direction method of multipliers
the Fortin and Glowinski's constant
global convergence
Article.40.pdf
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Stability of impulsive differential systems with state-dependent impulses via the linear decomposition method
Stability of impulsive differential systems with state-dependent impulses via the linear decomposition method
en
en
In this paper, we discuss the stability problem of the impulsive differential systems with state-dependent impulses. By using the linear decomposition methods, some sufficient conditions ensuring stability of the impulsive differential systems with state-dependent impulses are obtained and the estimate of the solution of such nonlinear systems is also acquired. Our results improve and generalize some of the known results given in earlier references. An example is given to demonstrate our results.
5052
5063
Jingting
Hu
School of Mathematical Sciences
University of Jinan
P. R. China
Guixia
Sui
Primary Education Department
Department of Mathematics, College of Arts and Science Faculty
Jinan Preschool Education College
Abu Dhabi University
P. R. China
United Arab Emirates
Haydar
Akca
Department of Mathematics, College of Arts and Science Faculty
Abu Dhabi University
United Arab Emirates
Xiaodi
Li
School of Mathematics and Statistics
Shandong Normal University
P. R. China
lxd@sdnu.edu.cn
Stability
impulsive differential systems
state-dependent impulses
linear decomposition methods
Article.41.pdf
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]
Lyapunov-type inequalities for certain higher order fractional differential equations
Lyapunov-type inequalities for certain higher order fractional differential equations
en
en
This paper generalizes the well-known Lyapunov-type inequality for certain higher
order fractional differential equations. The investigation is based on a construction of Green's functions and finding its corresponding maximum value. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.
5064
5071
Xuhuan
Wang
Department of Education Science
Pingxiang University
China
wangxuhuan84@163.com
Youhua
Peng
Department of Mathematics
Pingxiang University
China
pengyouh@126.com
Wanchun
Lu
Department of Mathematics
Pingxiang University
China
luwanchun540@163.com
Fractional differential equations
Lyapunov-type inequality
Green's function
boundary value problem
Article.42.pdf
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]
A new class of partially degenerate Hermite-Genocchi polynomials
A new class of partially degenerate Hermite-Genocchi polynomials
en
en
In this paper, firstly we introduce not only partially degenerate
Hermite-Genocchi polynomials, but also a new generalization of degenerate
Hermite-Genocchi polynomials. Secondly, we investigate some behaviors of
these polynomials. Furthermore, we establish some implicit summation
formulae and symmetry identities by making use of the generating function of
partially degenerate Hermite-Genocchi polynomials. Finally, some results
obtained here extend well-known summations and identities which we stated in
the paper.
5072
5081
Waseem A.
Khan
Department of Mathematics, Faculty of Science
Integral University
India
waseem08_khan@rediffmail.com
Serkan
Araci
Department of Economics, Faculty of Economics, Administrative and Social Science
Hasan Kalyoncu University
Turkey
mtsrkn@hotmail.com
Mehmet
Acikgoz
Department of Mathematics, Faculty of Arts and Science
University of Gaziantep
Turkey
acikgoz@gantep.edu.tr
Hiba
Haroon
Department of Mathematics, Faculty of Science
Integral University
India
hibaharoon786@gmail.com
Hermite polynomials
partially degenerate Genocchi polynomials
partially degenerate Hermite-Genocchi polynomials
summation formula
symmetric identities
Article.43.pdf
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]
The extremal iteration solution to a coupled system of nonlinear conformable fractional differential equations
The extremal iteration solution to a coupled system of nonlinear conformable fractional differential equations
en
en
In this paper, we consider a coupled system of nonlinear conformable fractional differential equations by using the comparison principle and the monotone iterative technique combined with the method of upper and lower solutions:
\[
\left\{\begin{aligned}
x^{(\alpha)}(t)=f(t,x(t),y(t)), t\in[a,b],\\
y^{(\alpha)}(t)=g(t,y(t),x(t)), t\in[a,b],\\
x(a)=x_0^*,\quad y(a)=y_0^*,
\end{aligned}
\right.
\]
where \(f,\,g\in C([a,b]\times\mathbb{R}\times\mathbb{R},\mathbb{R}),\ x_0^*,\,y_0^*\in\mathbb{R},\ x_0^*\le y_0^*,
\ x^{(\alpha)},\,y^{(\alpha)}\) are the conformable fractional derivatives with \(0<\alpha\le 1\).
We obtain the existence of extremal iteration solution to the system,
and the main results are examined by the help of an example.
5082
5089
Suli
Liu
Department of Mathematics
Department of Mathematical and Statistical Sciences
Jilin University
University of Alberta
P. R. China
Canada
liusl15@mails.jlu.edu.cn
Han
Wang
Department of Mathematics
Jilin University
P. R. China
hanwang15@mails.jlu.ed.cn
Xiaoping
Li
Institute of Mathematics and Finance
Xiangnan University
P. R. China
lxp418@126.com
Huilai
Li
Department of Mathematics
Jilin University
P. R. China
lihuilai@jlu.edu.cn
Nonlinear conformable fractional differential equations
extremal system of solutions
monotone iterative method
comparison principle
upper and lower solutions
Article.44.pdf
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T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66
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D. R. Anderson, R. I. Avery, Fractional-order boundary value problem with Sturm-Liouville boundary conditions, Electron. J. Differential Equations, 2015 (2015), 1-10
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H. Khan, H. Jafari, D. Baleanu, R. A. Khan, A. Khan, On Iterative Solutions and Error Estimations of a Coupled System of Fractional Order Differential-Integral Equations with Initial and Boundary Conditions, Differ. Equ. Dyn. Syst., 2017 (2017), 1-13
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W. Zhang, Z. Bai, S. Sun , Extremal solutions for some periodic fractional differential equations, Adv. Difference Equ., 2016 (2016), 1-8
]
Global best approximate solutions for set-valued cyclic \(\alpha\)-\(F\)-contractions
Global best approximate solutions for set-valued cyclic \(\alpha\)-\(F\)-contractions
en
en
In this paper, we introduce the concepts of multivalued cyclic
\(\alpha\)-\(F\) contraction and triangular \(\alpha\)-orbital
admissible mappings. We use these concepts to find global best
approximation solutions in a metric space with proximally complete
property. We also provide some nontrivial examples to support our
results. As an application, we obtain best proximity point results
in partially ordered metric spaces and best proximity point
theorems for single-valued mappings. We also prove fixed point results for multivalued and single-valued \(\alpha\)-type \(F\)-contractions.
5090
5107
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Iram
Iqbal
Department of Mathematics
University of Sargodha
Pakistan
irami@uos.edu.pk
Proximally complete pair
cyclic \(\alpha\)-\(F\)-contraction
cyclical Cauchy sequence
best proximity point
Article.45.pdf
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]
On \(S_{\alpha }^{\beta }\left( \theta \right)\)-convergence and strong \(N_{\alpha }^{\beta }\left( \theta ,p\right)\)-summability
On \(S_{\alpha }^{\beta }\left( \theta \right)\)-convergence and strong \(N_{\alpha }^{\beta }\left( \theta ,p\right)\)-summability
en
en
In the papers [M. Et, H.Şengül, Filomat, \({\bf 28}\) (2014), 1593--1602] and [H. Şengül, M. Et, Acta Math. Sci. Ser. B Engl. Ed., \({\bf 34}\) (2014), 473--482], we
defined the spaces of \(S^{\alpha }\left( \theta \right) \)-convergent
and strongly \(N^{\alpha }\left( \theta ,p\right) \)-summable sequences. In this paper these spaces are
generalized to the space of \(S_{\alpha }^{\beta }\left( \theta \right)\)-convergent sequences and the space of strongly \(N_{\alpha }^{\beta }\left( \theta ,p\right)\)-summable sequences and are given some inclusion relationships among these spaces.
keywords
5108
5115
Hacer
Şengül
Department of Mathematics
Siirt University 56100
Turkey
hacer.sengul@hotmail.com
Lacunary sequence
statistical convergence
Cesàro summability
Article.46.pdf
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]
Nonlinear stochastic analysis for a stochastic SIS epidemic model
Nonlinear stochastic analysis for a stochastic SIS epidemic model
en
en
This paper considers a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model with nonlinear saturated incidence. The threshold conditions for disease extinction and stochastic permanence are obtained by using nonlinear stochastic analysis for Feller's test and the canonical probability method. Consequently, this improves and extends some previous results obtained by using Lyapunov method. A series of numerical simulations are carried out to illustrate our theoretical findings.
5116
5124
Fei
Li
College of Mathematics and Systems Science
Shandong University of Science and Technology
P. R. China
lifei930512@163.com
Xinzhu
Meng
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology
Shandong University of Science and Technology
Shandong University of Science and Technology
P. R. China
P. R. China
mxz721106@sdust.edu.cn
Yujun
Cui
College of Mathematics and Systems Science
Shandong University of Science and Technology
P. R. China
cyj720201@163.com
Stochastic SIS epidemic model
Feller's test
stochastic permanence
nonlinear saturated incidence
Article.47.pdf
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I. Karatzas, S. E. Shreve, Brownian motion and stochastic calculus, Springer, New York (1988)
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Q. Liu, D.-Q. Jiang, N.-Z. Shi, T. Hayat, B. Ahmad, Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence, Phys. A, 476 (2017), 58-69
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J.-L. Lv, K. Wang, Almost sure permanence of stochastic single species models, J. Math. Anal. Appl., 422 (2015), 675-683
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H.-J. Ma, Y.-M. Jia , Stability analysis for stochastic differential equations with infinite Markovian switchings, J. Math. Anal. Appl., 435 (2016), 593-605
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W.-B. Ma, M. Song, Y. Takeuchi , Global stability of an SIR epidemicmodel with time delay, Appl. Math. Lett., 17 (2004), 1141-1145
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X.-R. Mao , Stochastic Differential Equations and Applications, Woodhead Publishing, Cambridge (2007)
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X.-Z. Meng, L.-S. Chen, B. Wu , A delay SIR epidemic model with pulse vaccination and incubation times, Nonlinear Anal., Real World Appl., 11 (2010), 88-98
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A.-Q. Miao, X.-Y. Wang, T.-Q. Zhang, W. Wang, B. G. S. A. Pradeep, Dynamical analysis of a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis, Adv. Difference Equ., 2017 (2017), 1-27
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J. J. Nieto, A. Ouahab, R. Rodríguez-López, Random fixed point theorems in partially ordered metric spaces, Fixed Point Theory Appl., 2016 (2016), 1-19
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C.-Q. Xu, S.-L. Yuan, An analogue of break-even concentration in a simple stochastic chemostat model, Appl. Math. Lett., 48 (2015), 62-68
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]
Fixed points for \(\varphi _{E}\)-Geraghty contractions
Fixed points for \(\varphi _{E}\)-Geraghty contractions
en
en
In this paper, we introduce the new concept of a generalization of
contraction so-called \(\varphi _{E}\)-Geraghty contraction and we establish a
fixed point theorem for such mappings in complete metric spaces.
5125
5131
Andreea
Fulga
Department of Mathematics and Computer Sciences
Transilvania University of Brasov
Romania
afulga@unitbv.ro
Alexandrina Maria
Proca
Department of Mathematics and Computer Sciences
Transilvania University of Brasov
Romania
alexproca@unitbv.ro
\(\varphi _{E}\)-Geraghty contractions mapping
fixed point
contraction
Article.48.pdf
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]