Viscosity approximation methods for generalized equilibrium problems and fixed point problems

被引：53

作者：

Ceng, Lu-Chuan ^{[2
]}

Ansari, Qamrul Hasan ^{[3
,4
]}

Yao, Jen-Chih ^{[1
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[4] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2009年 / 43卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Viscosity approximation method; Generalized equilibrium problem; Fixed points; Nonexpansive mappings; Strong convergence; VARIATIONAL-LIKE INEQUALITIES; NONEXPANSIVE-MAPPINGS; ALGORITHMS; THEOREM;

D O I：

10.1007/s10898-008-9342-6

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

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

页码：487 / 502

页数：16

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