]>
2016
9
8
ISSN 2008-1898
158
A general implicit iteration for finding fixed points of nonexpansive mappings
A general implicit iteration for finding fixed points of nonexpansive mappings
en
en
The aim of the paper is to construct an iterative method for finding the fixed points of nonexpansive
mappings. We introduce a general implicit iterative scheme for finding an element of the set of fixed points
of a nonexpansive mapping defined on a nonempty closed convex subset of a real Hilbert space. The strong
convergence theorem for the proposed iterative scheme is proved under certain assumptions imposed on the
sequence of parameters. Our results extend and improve the results given by Ke and Ma [Y. Ke, C. Ma,
Fixed Point Theory Appl., 2015 (2015), 21 pages], Xu et al. [H. K. Xu, M. A. Alghamdi, N. Shahzad, Fixed
Point Theory Appl., 2015 (2015), 12 pages], and many others.
5157
5168
D. R.
Sahu
Department of Mathematics, Institute of Science
Banaras Hindu University
India
drsahudr@gmail.com
Shin Min
Kang
Center for General Education
Department of Mathematics and the RINS
China Medical University
Gyeongsang National University
Taiwan
Korea
smkang@gnu.ac.kr
Ajeet
Kumar
Department of Mathematics, Institute of Science
Banaras Hindu University
India
ajeetbhu09@gmail.com
Sun Young
Cho
Department of Mathematics
Gyeongsang National University
Korea
ooly61@yahoo.co.kr
Metric projection mapping
nonexpansive mapping
variational inequality
viscosity method
implicit rules.
Article.1.pdf
[
[1]
R. P. Agarwal, D. O'Regan, D. R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications, Topological Fixed Point Theory and Its Applications, Springer, New York (2009)
##[2]
M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H. K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory and Appl., 2014 (2014), 1-9
##[3]
G. Bader, P. Deu hard, A semi-implicit mid-point rule for stiff systems of ordinary differential equations, Numer. Math., 41 (1983), 373-398
##[4]
L. C. Ceng, Q. H. Ansari, J. C. Yao, Some iterative methods for finding fixed points and for solving constrained convex minimization problems, Nonlinear Anal., 74 (2011), 5286-5302
##[5]
P. Deu hard, Recent progress in extrapolation methods for ordinary differential equations, SIAM Rev., 27 (1985), 505-535
##[6]
K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
##[7]
Y. Ke, C. Ma, The generalized viscosity implicit rules of nonexpansive mappings in Hilbert spaces, Fixed Point Theory and Appl., 2015 (2015), 1-21
##[8]
A. Latif, D. R. Sahu, Q. H. Ansari, Variable KM-like algorithms for fixed point problems and split feasibility problems, Fixed Point Theory and Appl., 2014 (2014), 1-20
##[9]
A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55
##[10]
S. Somalia, Implicit midpoint rule to the nonlinear degenerate boundary value problems, Int. J. Comput. Math., 79 (2002), 327-332
##[11]
H. K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[12]
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 and Appl., 2015 (2015), 1-12
##[13]
I. Yamada, The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings, Inherently parallel algorithms in feasibility and optimization and their applications, Haifa, (2000), Stud. Comput. Math., North-Holland, Amsterdam, 2001 (2001), 473-504
##[14]
Y. Yao, R. P. Agarwal, M. Postolache, Y. C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory and Appl., 2014 (2014), 1-14
##[15]
Y. Yao, Y. C. Liou, T. L. Lee, N. C. Wong, An iterative algorithm based on the implicit midpoint rule for nonexpansive mappings, J. Nonlinear Convex Anal., 17 (2016), 655-668
##[16]
Y. Yao, Y. C. Liou, J. C. Yao, Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction, Fixed Point Theory and Appl., 2015 (2015), 1-19
##[17]
Y. Yao, M. Postolache, Y. C. Liou, Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory and Appl., 2013 (2013), 1-12
##[18]
Y. Yao, N. Shahzad, Y. C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theory and Appl., 2015 (2015), 1-15
]
Variational principle for a three-point boundary value problem
Variational principle for a three-point boundary value problem
en
en
A variational principle is established for a three-point boundary value problem. The stationary condition
includes not only the governing equation but also the natural boundary conditions. The paper reveals that
not every boundary condition adopts a variational formulation, and the existence and uniqueness of the
solutions of a three-point boundary value problem can be revealed by its variational formulation.
5169
5174
Hong-Yan
Liu
School of Fashion Technology
National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering
Zhongyuan University of Technology
Soochow University
China
China
phdliuhongyan@yahoo.com
Ji-Huan
He
National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering
Soochow University
China
hejihuan@suda.edu.cn
Zhi-Min
Li
Rieter (China) Textile Instrument Co.
China
Variational theory
boundary value problem
semi-inverse method
natural boundary condition.
Article.2.pdf
[
[1]
U. Akcan, N. A. Hamal, Existence of concave symmetric positive solutions for a three-point boundary value problem, Adv. Difference Equ., 2014 (2014), 1-12
##[2]
F. Geng, Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method, Appl. Math. Comput., 215 (2009), 2095-2102
##[3]
J. H. He, Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons Fractals, 19 (2004), 847-851
##[4]
J. H. He, Variational approach to impulsive differential equations using the semi-inverse method, Zeitschrift für Naturforschung A, 66 (2011), 632-634
##[5]
J. H. He, Asymptotic methods for solitary solutions and compactons, Abstr. Appl. Anal., 2012 (2012), 1-130
##[6]
Y. Hu, J. H. He, On fractal space-time and fractional calculus, Thermal Sci., 20 (2016), 773-777
##[7]
Z. Jia, M. Hu, Q. Chen, Variational principle for unsteady heat conduction equation, Thermal Sci., 18 (2014), 1045-1047
##[8]
X. W. Li, Y. Li, J. H. He, On the semi-inverse method and variational principle, Thermal Sci., 17 (2013), 1565-1568
##[9]
M. Mohamed, B. Thompson, M. S. Jusoh, First-order three-point boundary value problems at resonance, J. Comput. Appl. Math., 235 (2011), 4796-4801
##[10]
Y. P. Sun, Existence of triple positive solutions for a third-order three-point boundary value problem, J. Comput. Appl. Math., 221 (2008), 194-201
##[11]
X. C. Zhong, Q. A. Huang, Approximate solution of three-point boundary value problems for second-order ordinary differential equations with variable coefficients, Appl. Math. Comput., 247 (2014), 18-29
]
Strong convergence for a common solution of variational inequalities, fixed point problems and zeros of finite maximal monotone mappings
Strong convergence for a common solution of variational inequalities, fixed point problems and zeros of finite maximal monotone mappings
en
en
In this paper, by the strongly positive linear bounded operator technique, a new generalized Mann-type
hybrid composite extragradient CQ iterative algorithm is first constructed. Then by using the algorithm,
we find a common element of the set of solutions of the variational inequality problem for a monotone,
Lipschitz continuous mapping, the set of zeros of two families of finite maximal monotone mappings and
the set of fixed points of an asymptotically \(\kappa\)-strict pseudocontractive mappings in the intermediate sense
in a real Hilbert space. Finally, we prove the strong convergence of the iterative sequences, which extends
and improves the corresponding previous works.
5175
5188
Yang-Qing
Qiu
Department of Mathematics
Shanghai Normal University
China
qiuyangqing@sohu.com
Jin-Zuo
Chen
Department of Mathematics
Shanghai Normal University
China
chanjanegeoger@163.com
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University
China
zenglc@hotmail.com
Hybrid method
extragradient method
proximal method
zeros
strong convergence.
Article.3.pdf
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[1]
H. H. Bauschke, P. L. Combettes, A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces, Math. Oper. Res., 26 (2001), 248-264
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L. C. Ceng, S. M. Guu, J. C. Yao, Hybrid viscosity CQ method for finding a common solution of a variational inequality, a general system of variational inequalities, and a fixed point problem, Fixed Point Theory and Appl., 2013 (2013), 1-25
##[3]
L. C. Ceng, S. M. Guu, J. C. Yao, Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense, J. Global Optim., 60 (2014), 617-634
##[4]
L. C. Ceng, C. W. Liao, C. T. Pang, C. F. Wen, Multistep hybrid iterations for systems of generalized equilibria with constraints of several problems, Abstr. Appl. Anal., 2014 (2014), 1-27
##[5]
K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
##[6]
H. Iiduka, W. Takahashi, Strong convergence theorem by a hybrid method for nonlinear mappings of nonexpansive and monotone type and applications, Adv. Nonlinear Var. Inequal., 9 (2006), 1-10
##[7]
G. M. Korpelevich, The extragradient method for finding saddle points and other problems,, Matecon, 12 (1976), 747-756
##[8]
G. Marino, H. K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 31 (2006), 43-52
##[9]
N. Nadezhkina, W. Takahashi, Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings, SIAM J. Optim., 16 (2006), 1230-1241
##[10]
X. Qin, M. Shang, S. M. Kang, Strong convergence theorems of modified Mann iterative process for strict pseudo- contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 1257-1264
##[11]
Y. Q. Qiu, L. C. Ceng, J. Z. Chen, H. Y. Hu, Hybrid iterative algorithms for two families of finite maximal monotone mappings, Fixed Point Theory and Appl., 2015 (2015), 1-18
##[12]
J. Radon, Theorie und anwendungen der absolut additiven mengenfunktionen, Wien. Ber., 122 (1913), 1295-1438
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R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 149 (1970), 75-88
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R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optimization, 14 (1976), 877-898
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D. R. Sahu, H. K. Xu, J. C. Yao, Asymptotically strict pseudocontractive mappings in the intermediate sense, Nonlinear Anal., 70 (2009), 3502-3511
##[16]
L. Wei, R. Tan, Strong and weak convergence theorems for common zeros of finite accretive mappings, Fixed Point Theory and Appl., 2014 (2014), 1-17
##[17]
Y. Yao, G. Marino, L. Muglia, A modified Korpelevich's method convergent to the minimum-norm solution of a variational inequality, Optimization, 63 (2014), 559-569
##[18]
Y. Yao, G. Marino, H. K. Xu, Y. C. Liou, Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces, J. Inequal. Appl., 2014 (2014), 1-14
##[19]
Y. Yao, M. Postolache, S. M. Kang, Strong convergence of approximated iterations for asymptotically pseudocontractive mappings, Fixed Point Theory and Appl., 2014 (2014), 1-13
##[20]
E. Zeidler, Nonlinear functional analysis and its applications, II/B: Nonlinear monotone Operators, Springer-Verlag, Berlin (1990)
]
Almost monotone contractions on weighted graphs
Almost monotone contractions on weighted graphs
en
en
Almost contraction mappings were introduced as an extension to the contraction mappings for which
the conclusion of the Banach contraction principle (BCP in short) holds. In this paper, the concept of
monotone almost contractions defined on a weighted graph is introduced. Then a fixed point theorem for
such mappings is given.
5189
5195
Monther R.
Alfuraidan
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Saudi Arabia
monther@kfupm.edu.sa
Mostafa
Bachar
Department of Mathematics, College of Sciences
King Saud University
Saudi Arabia
mbachar@ksu.edu.sa
Mohamed A.
Khamsi
Department of Mathematical Sciences
University of Texas at El Paso
U. S. A.
mohamed@utep.edu
Almost contraction
directed graph
fixed point
monotone mapping
multivalued mapping.
Article.4.pdf
[
[1]
M. R. Alfuraidan , Remarks on monotone multivalued mappings on a metric space with a graph, J. Inequal. Appl., 2015 (2015), 1-7
##[2]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
##[3]
V. Berinde, On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., 19 (2003), 7-22
##[4]
V. Berinde, M. Păcurar, Fixed points and continuity of almost contractions, Fixed Point Theory, 9 (2008), 23-34
##[5]
S. K. Chatterjea , Fixed-point theorems, C. R. Acad. Bulgare Sci., 25 (1972), 727-730
##[6]
S. M. El-Sayed, A. C. M. Ran , On an iteration method for solving a class of nonlinear matrix equations , SIAM J. Matrix Anal. Appl., 23 (2002), 632-645
##[7]
Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl., 317 (2006), 103-112
##[8]
K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
##[9]
M. T. Goodrich, R. Tamassia, Algorithm design: foundations, analysis and internet examples, John Wiley & Sons, Inc., New York (2001)
##[10]
J. Jachymski, The contraction principle for mappings on a metric space with a graph , Proc. Amer. Math. Soc., 136 (2008), 1359-1373
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R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76
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M. A. Khamsi, W. A. Kirk , An introduction to metric spaces and fixed point theory, Pure and Applied Mathematics, Wiley-Interscience, New York (2001)
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D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334 (2007), 132-139
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S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488
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J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
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A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443
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I. A. Rus, Generalized contractions, Seminar on Fixed Point Theory, 3 (1983), 1-130, Preprint, 83-3, Univ. ''Babe-Bolyai'', Cluj-Napoca (1983)
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I. A. Rus, Generalized contractions and applications, Cluj University Press, Cluj-Napoca (2001)
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M. R. Tasković, Osnove teorije fiksne take, (Serbo-Croatian) [Foundations of fixed-point theory] With an English summary, Matematicka Biblioteka [Mathematical Library], Zavod za Udzbenike i Nastavna Sredstva, Belgrade, 1986 (1986), 1-272
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M. Turinici, Fixed points for monotone iteratively local contractions, Demonstratio Math., 19 (1986), 171-180
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X. A. Udo-utun, Z. U. Siddiqui, M. Y. Balla, An extension of the contraction mapping principle to Lipschitzian mappings, Fixed Point Theory Appl., 2015 (2015), 1-7
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D. W. Wallis , A beginner's guide to graph theory , Second edition, Birkhäuser Boston, Inc., Boston (2007)
##[23]
T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math. (Basel), 23 (1972), 292-298
]
A study on a class of q-Euler polynomials under the symmetric group of degree n
A study on a class of q-Euler polynomials under the symmetric group of degree n
en
en
Motivated by the paper of Kim et al. [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, D. V. Dolgy, J.
Nonlinear Sci. Appl., 9 (2016), 1077-1082], we study a class of q-Euler polynomials earlier given by Kim et
al. in [T. Kim, Y. H. Kim, K. W. Hwang, Proc. Jangjeon Math. Soc., 12 (2009), 77-92]. We derive some
new symmetric identities for q-extension of \(\lambda\)-Euler polynomials, using fermionic p-adic invariant integral
over the p-adic number field originally introduced by Kim in [T. Kim, Russ. J. Math. Phys., 16 (2009),
484-491], under symmetric group of degree n denoted by \(S_n\).
5196
5201
Serkan
Araci
Department of Economics, Faculty of Economics, Administrative and Social Science
Hasan Kalyoncu University
Turkey
mtsrkn@hotmail.com
Ugur
Duran
Department of Mathematics, Faculty of Arts and Science
University of Gaziantep
Turkey
duran.ugur@yahoo.com
Mehmet
Acikgoz
Department of Mathematics, Faculty of Arts and Science
University of Gaziantep
Turkey
acikgoz@gantep.edu.tr
Symmetric identities
q-extension of \(\lambda\)-Euler polynomials
fermionic p-adic invariant integral on \(\mathbb{Z}_p\)
invariant under \(S_n\).
Article.5.pdf
[
[1]
E. Ağyüz, M. Acikgoz, S. Araci, A symmetric identity on the q-Genocchi polynomials of higher-order under third dihedral group \(D_3\), Proc. Jangjeon Math. Soc., 18 (2015), 177-187
##[2]
U. Duran, M. Acikgoz, S. Araci, Symmetric identities involving weighted q-Genocchi polynomials under \(S_4\), Proc. Jangjeon Math. Soc., 18 (2015), 455-465
##[3]
Y. He, S. Araci, Sums of products of Apostol-Bernoulli and Apostol-Euler polynomials, Adv. Difference Equ., 2014 (2014), 1-13
##[4]
Y. He, S. Araci, H. M. Srivastava, M. Acikgoz, Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials, Appl. Math. Comput., 262 (2015), 31-41
##[5]
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys.,, 9 (2002), 288-299
##[6]
T. Kim, Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., 16 (2009), 484-491
##[7]
T. Kim, Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., 16 (2009), 93-96
##[8]
D. S. Kim, T. Kim, Some identities of symmetry for q-Bernoulli polynomials under symmetric group of degree n, Ars Combin., 126 (2016), 435-441
##[9]
T. Kim, Y. H. Kim, K. W. Hwang, On the q-extensions of the Bernoulli and Euler numbers, related identities and Lerch zeta function, Proc. Jangjeon Math. Soc., 12 (2009), 77-92
##[10]
T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, D. V. Dolgy, Some identities of q-Euler polynomials under the symmetric group of degree n, J. Nonlinear Sci. Appl., 9 (2016), 1077-1082
##[11]
D. Q. Lu, H. M. Srivastava, Some series identities involving the generalized Apostol type and related polynomials, Comput. Math. Appl., 62 (2011), 3591-3602
]
On best proximity points for various \(\alpha\)-proximal contractions on metric-like spaces
On best proximity points for various \(\alpha\)-proximal contractions on metric-like spaces
en
en
We establish some best proximity points for various \(\alpha\)-proximal contractive non-self-mappings in the class
of metric-like spaces. We provide concrete examples. We also present some best proximity point theorems in
metric (metric-like) spaces endowed with a graph and in partially ordered metric spaces.
5202
5218
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research
University of Dammam
China Medical University Hospital, China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Abdelbasset
Felhi
Department of Mathematics, College of Sciences
King Faisal University
Saudi Arabia
afelhi@kfu.edu.sa
Metric-like
best proximity point
fixed point
controlled proximal contraction.
Article.6.pdf
[
[1]
A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory and Appl., 2012 (2012), 1-10
##[2]
H. Aydi, A. Felhi, E. Karapinar, S. Sahmim, Hausdorff metric-like, generalized Nadler's fixed point theorem on metric-like spaces and application, Micolc Math. Notes, ((In press)), -
##[3]
H. Aydi, A. Felhi, S. Sahmim, Fixed points of multivalued nonself almost contractions in metric-like spaces, Math. Sci. (Springer), 9 (2015), 103-108
##[4]
H. Aydi, E. Karapinar, Fixed point results for generalized \(\alpha-\psi\)-contractions in metric-like spaces and applications, Electron. J. Differential Equations, 2015 (2015), 1-15
##[5]
C. Chen, J. Dong, C. Zhu, Some fixed point theorems in b-metric-like spaces, Fixed Point Theory and Appl., 2015 (2015), 1-10
##[6]
M. Cvetković, E. Karapınar, V. Rakocević, Some fixed point results on quasi-b-metric-like spaces, J. Inequal. Appl., 2015 (2015), 1-17
##[7]
A. Felhi, H. Aydi, Best proximity points and stability results for controlled proximal contractive set valued mappings, Fixed Point Theory and Appl., 2016 (2016), 1-23
##[8]
M. Jleli, E. Karapınar, B. Samet, Best proximity points for generalized \(\alpha-\psi\)-proximal contractive type mappings, J. Appl. Math., 2013 (2013), 1-10
##[9]
S. Karpagam, S. Agrawal, Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps, Non-linear Anal., 74 (2011), 1040-1046
##[10]
W. K. Kim, S. Kum, K. H. Lee, On general best proximity pairs and equilibrium pairs in free abstract economies, Nonlinear Anal., 68 (2008), 2216-2227
##[11]
W. A. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim., 24 (2003), 851-862
##[12]
C. Mongkolkeha, P. Kumam, Best proximity point theorems for generalized cyclic contractions in ordered metric spaces, J. Optim. Theory Appl., 155 (2012), 215-226
##[13]
H. K. Nashine, P. Kumam, C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory and Appl., 2013 (2013), 1-11
##[14]
V. S. Raj, P. Veeramani, Best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74 (2011), 4804-4808
##[15]
S. Sadiq Basha, P. Veeramani, Best proximity pairs and best approximations, Acta Sci. Math. (Szeged), 63 (1997), 289-300
##[16]
S. Sadiq Basha, P. Veeramani, Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory, 103 (2000), 119-129
##[17]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[18]
J. Zhang, Y. Su, Q. Cheng, A note on 'A best proximity point theorem for Geraghty-contractions', Fixed Point Theory and Appl., 2013 (2013), 1-4
]
On monotone mappings in modular function spaces
On monotone mappings in modular function spaces
en
en
We prove the existence of fixed points of monotone \(\rho\)-nonexpansive mappings in \(\rho\)-uniformly convex
modular function spaces. This is the modular version of Browder and Göhde fixed point theorems for
monotone mappings. We also discuss the validity of this result in modular function spaces where the
modular is uniformly convex in every direction. This property has never been considered in the context of
modular spaces.
5219
5228
Buthinah A. Bin
Dehaish
Department of Mathematics, Faculty of Sciences
King Abdulaziz University
Saudi Arabia
bbendehaish@kau.edu.sa
Mohamed A.
Khamsi
Department of Mathematics and Statistics
Department of Mathematical Sciences
King Fahd University of Petroleum and Minerals
The University of Texas at El Paso
Saudi Arabia
U. S. A.
mohamed@utep.edu
Fixed point
Krasnoselskii iteration
modular function spaces
monotone mapping
nonexpansive mapping
partially ordered
uniformly convex
uniformly convex in every direction.
Article.7.pdf
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M. Bachar, M. A. Khamsi , Fixed points of monotone mappings and application to integral equations, Fixed Point Theory Appl., 2015 (2015), 1-7
##[3]
S. Banach , Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math., 3 (1922), 133-181
##[4]
B. A. Bin Dehaish, W. M. Kozlowski, Fixed point iteration processes for asymptotic pointwise nonexpansive mapping in modular function spaces, Fixed Point Theory Appl., 2012 (2012), 1-23
##[5]
F. E. Browder , Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 1041-1044
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S. Chen , Geometry of Orlicz spaces , With a preface by Julian Musielak, Dissertationes Math. (Rozprawy Mat.), 356 (1996), 1-204
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S. M. El-Sayed, A. C. M. Ran, On an iteration method for solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl., 23 (2002), 632-645
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A. L. Garkavi, On the optimal net and best cross-section of a set in a normed space, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 26 (1962), 87-106
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K. Goebel, W. A. Kirk, Topics in metric fixed point theory , Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
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D. Göhde, Zum Prinzip der kontraktiven Abbildung, (German) Math. Nachr., 30 (1965), 251-258
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H. Hudzik, A. Kamińska, M. Masty lo , Geometric properties of some Caldern-Lozanovski spaces and Orlicz-Lorentz spaces , Houston J. Math., 22 (1996), 639-663
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]
Calculations on topological degrees of semi-closed 1-set-contractive operators in M-PN-spaces and applications
Calculations on topological degrees of semi-closed 1-set-contractive operators in M-PN-spaces and applications
en
en
The aim of the paper is to study some calculating problems of topological degrees of semi-closed 1-set-
contractive operators in M-PN-spaces. Under some weak and natural conditions, several calculation results
are obtained. Finally, in order to verify the validity of our results, a support example is given at the end of
the paper.
5229
5237
Jiandong
Yin
Department of Mathematics
Nanchang University
P. R. China
yjdaxf@163.com
Pinghua
Yan
Department of Mathematics
Nanchang University
P. R. China
mathyph@163.com
Qianqian
Leng
Department of Mathematics
Nanchang University
P. R. China
13517914026@163.com
Topological degree
M-PN-space
semi-closed 1-set-contractive operator
fixed point.
Article.8.pdf
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C. Zhu, Several nonlinear operator problems in the Menger PN space, Nonlinear Anal., 65 (2009), 1281-1284
]
A multi-dimensional functional equation having cubic forms as solutions
A multi-dimensional functional equation having cubic forms as solutions
en
en
In this paper, we obtain some results on the m-variable cubic functional equation
\[f(2x_1 + y_1,..., 2x_m + y_m) + f(2x_1 - y_1,..., 2x_m - y_m)\\
= 2f(x_1 + y_1,..., x_m + y_m) + 2f(x_1 - y_1,..., x_m - y_m) + 12f(x_1,..., x_m).\]
The cubic form \(f(x_1,..., x_m) =
\sum_{1\leq i\leq j\leq k\leq m} a_{ijk}x_ix_jx_k\) is a solution of the above functional equation.
5238
5244
Won-Gil
Park
Department of Mathematics Education, College of Education
Mokwon University
Republic of Korea
wgpark@mokwon.ac.kr
Jae-Hyeong
Bae
Humanitas College
Kyung Hee University
Republic of Korea
jhbae@khu.ac.kr
Cubic form
solution
stability.
Article.9.pdf
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[1]
J.-H. Bae, W.-G. Park, A functional equation on homogeneous polynomials, J. Korean Soc. Math. Educ. Ser. B, 15 (2008), 103-110
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I.-S. Chang, Y.-S. Jung, Stability of a functional equation deriving from cubic and quadratic functions, J. Math. Anal. Appl., 283 (2003), 491-500
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H.-Y. Chu, D.-S. Kang, On the stability of an n-dimensional cubic functional equation, J. Math. Anal. Appl., 325 (2007), 595-607
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K.-W. Jun, H.-M. Kim, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Math. Anal. Appl., 274 (2002), 867-878
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K.-W. Jun, H.-M. Kim, I.-S. Chang, On the Hyers-Ulam stability of an Euler-Lagrange type cubic functional equation, J. Comput. Anal. Appl., 7 (2005), 21-33
]
On the fixed point theory in bicomplete quasi-metric spaces
On the fixed point theory in bicomplete quasi-metric spaces
en
en
We show that some important fixed point theorems on complete metric spaces as Browder's fixed point
theorem and Matkowski's fixed point theorem can be easily generalized to the framework of bicomplete
quasi-metric spaces. From these generalizations we deduce quasi-metric versions of well-known fixed point
theorems due to Krasnoselskiĭ and Stetsenko; Khan, Swalesh and Sessa; and Dutta and Choudhury, respectively. In fact, our approach shows that many fixed point theorems for \(\varphi\)-contractions on bicomplete
quasi-metric spaces, and hence on complete G-metric spaces, are actually consequences of the corresponding
fixed point theorems for complete metric spaces.
5245
5251
Carmen
Alegre
Instituto Universitario de Matemática Pura y Aplicada
Universitat Politècnica de València
Spain
calegre@mat.upv.es
Hacer
Dağ
Departamento de Matemática Aplicada
Universitat Politècnica de València
Spain
hada@doctor.upv.es
Salvador
Romaguera
Instituto Universitario de Matemática Pura y Aplicada
Departamento de Matemática Aplicada
Universitat Politècnica de València
Universitat Politècnica de València
Spain
Spain
sromague@mat.upv.es
Pedro
Tirado
Instituto Universitario de Matemática Pura y Aplicada
Universitat Politècnica de València
Spain
pedtipe@mat.upv.es
Quasi-metric space
bicomplete
\(\varphi\)-contraction
fixed point.
Article.10.pdf
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R. P. Agarwal, E. Karapınar, A. F. Roldán López de Hierro, Last remarks on G-metric spaces and related fixed point theorems, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Math. RACSAM, 110 (2016), 433-456
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H. Dag, G. Minak, I. Altun, Some fixed point results for multivalued F-contractions on quasi metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 2016 (2016), 1-11
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E. Karapınar, S. Romaguera, On the weak form of Ekeland’s variational principle in quasi-metric spaces, Topology Appl., 184 (2015), 54-60
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M. A. Krasnoselskiı, G. M. Vaınikko, P. P. Zabreıko, Y. B. Rutitskiı, V. Y. Stetsenko, Approximate solution of operator equations, Translated from the Russian by D. Louvish, Wolters-Noordhoff Publishing, Groningen (1972)
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H. P. A. Künzi, Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology, Handbook of the history of general topology, Hist. Topol., Kluwer Acad. Publ., Dordrecht, 3 (2001), 853-968
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A. Latif, S. A. Al-Mezel , Fixed point results in quasimetric spaces, Fixed Point Theory Appl., 2011 (2011), 1-8
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J. Marín, S. Romaguera, P. Tirado, Generalized contractive set-valued maps on complete preordered quasi-metric spaces, J. Funct. Spaces Appl., 2013 (2013), 1-6
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S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, II Iberoamerican Conference on Topology and its Applications (Morelia, 1997), Topology Appl., 98 (1999), 311-322
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S. Romaguera, M. P. Schellekens, O. Valero, Complexity spaces as quantitative domains of computation, Topology Appl., 158 (2011), 853-860
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S. Romaguera, O. Valero, Domain theoretic characterisations of quasi-metric completeness in terms of formal balls, Math. Structures Comput. Sci., 20 (2010), 453-472
]
Strong convergence theorem for common solutions to quasi variational inclusion and fixed point problems
Strong convergence theorem for common solutions to quasi variational inclusion and fixed point problems
en
en
In this paper, we consider a problem that consists of finding a common solution to quasi variational
inclusion and fixed point problems. We first present a simple proof to the strong convergence theorem
established by Zhang et al. recently. Next, we propose a new algorithm to solve such a problem. Under
some mild conditions, we establish the strong convergence of iterative sequence of the proposed algorithm.
5252
5258
Xianzhi
Tang
Department of of basic courses
Yellow River Conservancy Technical Institute
China
Huanhuan
Cui
Department of Mathematics
Luoyang Normal University
China
hhcui@live.cn
Variational inclusion
fixed point problem
inverse strongly monotone operator
nonexpansive mapping
multi-valued maximal monotone mapping.
Article.11.pdf
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H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal., 61 (2005), 341-350
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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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N. Nadezhkina, W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl., 128 (2006), 191-201
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W. Takahashi, M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl., 118 (2003), 417-428
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H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. (2), 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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L.-C. Zeng, J.-C. Yao, Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems, Taiwanese J. Math., 10 (2006), 1293-1303
##[11]
S.-S. Zhang, J. H. W. Lee, C. K. Chan, Algorithms of common solutions to quasi variational inclusion and fixed point problems, Appl. Math. Mech. (English Ed.), 29 (2008), 571-581
]
Multivalent guiding functions in the bifurcation problem of differential inclusions
Multivalent guiding functions in the bifurcation problem of differential inclusions
en
en
In this paper we use the multivalent guiding functions method to study the bifurcation problem for differential inclusions with convex-valued right-hand part satisfying the upper Carathéodory and the sublinear
growth conditions.
5259
5270
Sergey
Kornev
Faculty of Physics and Mathematics
Voronezh State Pedagogical University
Russia
kornev_vrn@rambler.ru
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics; and Research Center of Nonlinear Analysis and Optimization and Center for Fundamental Science
Kaohsiung Medical University
Taiwan
simplex_liou@hotmail.com
Differential inclusion
bifurcation of periodic solution
multivalent guiding function
topological degree.
Article.12.pdf
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[1]
P. S. Aleksandrov, B. A. Pasynkov, Vvedenie v teoriyu razmernosti: Vvedenie v teoriyu topologicheskikh prostranstv i obshchuyu teoriyu razmernosti, (Russian), [Introduction to dimension theory: An introduction to the theory of topological spaces and the general theory of dimension], Izdat. ''Nauka'', Moscow (1973)
##[2]
Y. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskiĭ, Introduction to the theory of multivalued maps and differential inclusions, (Russian) 2nd Ed., Librokom, Moscow (2011)
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K. Deimling , Multivalued differential equations, de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter and Co., Berlin (1992)
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A. Fryszkowski, Fixed point theory for decomposable sets, Topological Fixed Point Theory and Its Applications, Kluwer Academic Publishers, Dordrecht (2004)
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L. Górniewicz , Topological fixed point theory of multivalued mappings, Second edition, Topological Fixed Point Theory and Its Applications, Springer, Dordrecht (2000)
##[6]
M. Kamenskii, V. V. Obukhovskiĭ, P. Zecca, Condensing multivalued maps and semilinear differential inclusions in Banach spaces, De Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter and Co., Berlin (2001)
##[7]
S. V. Kornev, On the method of multivalent guiding functions for periodic solution of differential inclusions, Autom. Remote Control, 64 (2003), 409-419
##[8]
S. V. Kornev, Nonsmooth integral directing functions in the problems of forced oscillations, Translation of Avtomat. i Telemekh, (2015), 31-43, Autom. Remote Control, 76 (2015), 1541-1550
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S. V. Kornev, The method of generalized integral guiding function in the periodic problem of differential inclusions, (Russian) The Bulletin of Irkutsk State University. Mathematics, 13 (2015), 16-31
##[10]
S. V. Kornev , Multivalent guiding function in a problem on existence of periodic solutions of some classes of differential inclusions, Izv. Vyssh. Uchebn. Zaved. Mat., 11 (2016), 14-26
##[11]
S. V. Kornev , On asymptotics of solutions for differential inclusions with nonconvex right-hand side, (Russian) The Bulletin of Voronezh State University. Phisics. Mathematics, 1 (2016), 96-104
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S. V. Kornev, V. V. Obukhovskiĭ , On nonsmooth multivalent guiding functions, (Russian) Differ. Uravn., 39 (2003), 1497-1502, translation in Differ. Equ., 39 (2003), 1578-1584
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S. V. Kornev, V. V. Obukhovskiĭ, On some developments of the method of integral guiding functions, Funct. Differ. Equ., 12 (2005), 303-310
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S. V. Kornev, V. V. Obukhovskiĭ, Asymptotic behavior of solutions of differential inclusions and the method of guiding functions, Translation of Differ. Uravn., 51 (2015), 700-705, Differ. Equ., 51 (2015), 711-716
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S. V. Kornev, V. V. Obukhovskiĭ, J.-C. Yao, On asymptotics of solutions for a class of functional differential inclusions, Discuss. Math. Differ. Incl. Control Optim., 34 (2014), 219-227
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S. V. Kornev, V. V. Obukhovskiĭ, P. Zecca, Guiding functions and periodic solutions for inclusions with causal multioperators, Appl. Anal., 2016 (2016), 1-11
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M. A. Krasnosel'skiĭ, P. P. Zabreĭko, Geometrical methods of nonlinear analysis, Translated from the Russian by Christian C. Fenske, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin (1984)
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W. Kryszewski, Homotopy Properties of Set-Valued in Mappings, University Nicholas Copernicus Publishing, Toruń (1997)
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Z. Liu, N. V. Loi, V. V. Obukhovskiĭ , Existence and global bifurcation of periodic solutions to a class of differential variational inequalities, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 23 (2013), 1-10
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N. V. Loi, Z. Liu, V. V. Obukhovskiĭ , On an A-bifurcation theorem with application to a parameterized integro- differential system, Fixed Point Theory, 16 (2015), 127-141
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N. V. Loi, V. V. Obukhovskiĭ, J.-C. Yao, A bifurcation of solutions of nonlinear Fredholm inclusions involving CJ-multimaps with applications to feedback control systems, Set-Valued Var. Anal., 21 (2013), 247-269
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N. V. Loi, V. V. Obukhovskiĭ, J.-C. Yao, A multiparameter global bifurcation theorem with application to a feedback control system, Fixed Point Theory, 16 (2015), 353-370
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V. V. Obukhovskiĭ, M. Kamenskiĭ, S. V. Kornev, Y.-C. Liou, On asymptotics of solutions for some classes of differential inclusions via the generalized guiding functions method, submitted to J. Nonlin. Conv. Anal., (2016)
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]
On the Meir-Keeler-Khan set contractions
On the Meir-Keeler-Khan set contractions
en
en
This report is aim to investigate the fixed points of two classes of Meir-Keeler-Khan set contractions
with respect to the measure of noncompactness. The proved results extend a number of recently announced
theorems on the topic.
5271
5280
Chi-Ming
Chen
Department of Applied Mathematics
National Hsinchu University of Education
Taiwan
Erdal
Karapınar
Department of Mathematics
Atılım University
Turkey
erdalkarapinar@yahoo.com
Guang-Ting
Chen
Department of Applied Mathematics
National Hsinchu University of Education
Taiwan
Meir-Keeler-type set contraction
multivalued mapping
fixed points.
Article.13.pdf
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A. Aghajani, R. Allahyari, M. Mursaleen, A generalization of Darbo's theorem with application to the solvability of systems of integral equations, J. Comput. Appl. Math., 260 (2014), 68-77
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A. Aghajani, J. Banaś, N. Sabzali, Some generalizations of Darbo fixed point theorem and applications, Bull. Belg. Math. Soc. Simon Stevin, 20 (2013), 345-358
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A. Aghajani, M. Mursaleen, A. Shole Haghighi, Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness, Acta Math. Sci. Ser. B Engl. Ed., 35 (2015), 552-566
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A. Aghajani, N. Sabzali, Existence of coupled fixed points via measure of noncompactness and applications, J. Nonlinear Convex Anal., 15 (2014), 941-952
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N. Redjel, A. Dehici, Some results in fixed point theory and application to the convergence of some iterative processes, Fixed Point Theory and Appl., 2015 (2015), 1-17
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B. Samet, C. Vetro, P. Vetro, Some results on fixed points of \(\alpha-\psi\)-Ciric generalized multifunctions, Fixed Point Theory and Appl., 2013 (2013), 1-10
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Z. Wang, H. Li, Fixed point theorems and endpoint theorems for (\(\alpha,\psi\) )-Meir-Keeler-Khan multivalued mappings, Fixed Point Theory and Appl., 2016 (2016), 1-18
]
Quenching for a parabolic system with general singular terms
Quenching for a parabolic system with general singular terms
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en
In this paper, we study a parabolic system with general singular terms and positive Dirichlet boundary
conditions. Some sufficient conditions for finite-time quenching and global existence of the solutions are
obtained, and the blow-up of time-derivatives at the quenching point is verified. Furthermore, under some
appropriate hypotheses, we prove that the quenching point is only origin and quenching of the system is
non-simultaneous. Moreover, the estimate of quenching rate of the corresponding solution is established in
this article.
5281
5290
Haijie
Pei
College of Mathematics and Information
China West Normal University
P. R. China
Haijie-Pei@sohu.com
Zhongping
Li
College of Mathematics and Information
China West Normal University
P. R. China
Zhongping-Li@sohu.com
Quenching
quenching set
quenching rate
singular term
parabolic system.
Article.14.pdf
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]
Further result on \(\mathcal{H}_\infty\) state estimation of static neural networks with interval time-varying delay
Further result on \(\mathcal{H}_\infty\) state estimation of static neural networks with interval time-varying delay
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This paper considers the \(\mathcal{H}_\infty\) state estimation problem of static neural networks with interval timevarying
delay. By constructing a suitable Lyapunov-Krasovskii functional, the single-integral and doubleintegral
terms in the time derivative of the Lyapunov functional are handled by utilizing the inverses of
first-order and squared reciprocally convex parameters techniques. An improved delay dependent criterion
is established such that the error system is globally asymptotically stable with \(\mathcal{H}_\infty\) performance. The desired
estimator gain matrix and the optimal performance index are obtained via solving a convex optimization
problem subject to linear matrix inequalities. Two numerical examples are given to illustrate the effectiveness
of the proposed method.
5291
5305
Xiaojun
Zhang
School of Mathematics Sciences
University of Electronic Science and Technology of China
P. R. China
sczhxj@uestc.edu.cn
Xin
Wang
School of Information and Software Engineering
University of Electronic Science and Technology of China
P. R. China
Shouming
Zhong
School of Mathematics Sciences
University of Electronic Science and Technology of China
P. R. China
Static neural networks
\(\mathcal{H}_\infty\) state estimation
reciprocally convex approach
interval time-varying delay.
Article.15.pdf
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]
Fixed points of mixed non-monotone tripled operators in ordered Banach spaces and applications
Fixed points of mixed non-monotone tripled operators in ordered Banach spaces and applications
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This paper is concerned with a class of mixed non-monotone tripled operators under the general conditions
of ordering relations in ordered Banach spaces. By means of the cone theory and technique of
equivalent norms, the existence and uniqueness of fixed points for such tripled operators are established.
The proof method in this paper is different from those used in the former relevant theorems. At last, an
application is presented to illustrate our result. We extend some previous existing results.
5306
5315
Xiaoyan
Zhang
School of Mathematics
Shandong University
China
zxysd@sdu.edu.cn
Non-monotone tripled operator
cone theory
equivalent norms
fixed points
Banach spaces.
Article.16.pdf
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