Viscosity approximation methods for generalized equilibrium problems and fixed point problems

被引：0
作者：
Lu-Chuan Ceng
Qamrul Hasan Ansari
Jen-Chih Yao
机构：
[1] Shanghai Normal University,Department of Mathematics
[2] King Fahd University of Petroleum & Minerals,Department of Mathematics and Statistics
[3] Aligarh Muslim University,Department of Mathematics
[4] National Sun Yat-sen University,Department of Applied Mathematics
来源：
Journal of Global Optimization | 2009年 / 43卷
关键词：
Viscosity approximation method; Generalized equilibrium problem; Fixed points; Nonexpansive mappings; Strong convergence;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in the setting of Hilbert spaces. By using well-known Fan-KKM lemma, we derive the existence and uniqueness of a solution of the auxiliary problem for GEP. On account of this result and Nadler’s theorem, we propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping. Furthermore, it is proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping.
引用
收藏
页码：487 / 502
页数：15
相关论文
共 50 条
[21]   Hybrid viscosity methods for equilibrium problems, variational inequalities, and fixed point problems [J].
Ceng, L. C. ;
Latif, A. ;
Al-Mazrooei, A. E. .
APPLICABLE ANALYSIS, 2016, 95 (05) :1088-1117
[22]   An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems [J].
Petrusel, Adrian ;
Yao, Jen-Chih .
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2009, 7 (02) :335-347
[23]   Monotone variational inequalities, generalized equilibrium problems and fixed point methods [J].
Wang, Shenghua .
FIXED POINT THEORY AND APPLICATIONS, 2014,
[24]   A Viscosity of Cesaro Mean Approximation Methods for a Mixed Equilibrium, Variational Inequalities, and Fixed Point Problems [J].
Jitpeera, Thanyarat ;
Katchang, Phayap ;
Kumam, Poom .
FIXED POINT THEORY AND APPLICATIONS, 2011,
[25]   Viscosity iteration method for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings [J].
Inchan, Issara .
APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (06) :2949-2959
[26]   VISCOSITY APPROXIMATION METHODS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS [J].
Wang, Shenghua ;
Zhou, Haiyun ;
Song, Jianmin .
METHODS AND APPLICATIONS OF ANALYSIS, 2007, 14 (04) :405-420
[27]   An iterative approximation scheme for solving a split generalized equilibrium, variational inequalities and fixed point problems [J].
Sitthithakerngkiet, Kanokwan ;
Deepho, Jitsupa ;
Martinez-Moreno, Juan ;
Kumam, Poom .
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2017, 94 (12) :2373-2395
[28]   A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mappings [J].
Kumam, Poom ;
Katchang, Phayap .
NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2009, 3 (04) :475-486
[29]   A viscosity scheme for mixed equilibrium problems, variational inequality problems and fixed point problems [J].
Cai, Gang ;
Bu, Shangquan .
MATHEMATICAL AND COMPUTER MODELLING, 2013, 57 (5-6) :1212-1226
[30]   Fixed point solutions of generalized equilibrium problems for nonexpansive mappings [J].
Shehu, Y. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (03) :892-898
12345