Hybrid extragradient method for general equilibrium problems and fixed point problems in Hilbert space

被引：5
|
作者：
Inchan, Issara [1 ]
机构：
[1] Uttaradit Rajabhat Univ, Fac Sci & Technol, Dept Math & Comp, Uttaradit 53000, Thailand
来源：
NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2011年 / 5卷 / 03期
关键词：
Hybrid extragradient method; Nonexpansive mapping; Variational inequality problem; Equilibrium problem; Fixed points; VISCOSITY APPROXIMATION METHODS; STRONG-CONVERGENCE THEOREM; NONEXPANSIVE-MAPPINGS; MONOTONE MAPPINGS; WEAK-CONVERGENCE;
D O I：
10.1016/j.nahs.2010.10.005
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we introduce an iterative scheme by the hybrid methods for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of a variational inequality problem in a Hilbert space. Then, we prove the strongly convergent theorem by a hybrid extragradient method to the common element of the set of fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of a variational inequality problem. Our results extend and improve the results of Bnouhachem et al. [A. Bnouhachem, M. Aslam Noor, Z. Hao, Some new extragradient iterative methods for variational inequalities, Nonlinear Analysis (2008) doi:10.1016/j.na.2008.02.014] and many others. (C) 2010 Elsevier Ltd. All rights reserved.
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页码：467 / 478
页数：12
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