Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems

被引：6

作者：

Saewan, Siwaporn ^{[1
]}

Kumam, Poom ^{[2
]}

Cho, Yeol Je ^{[3
,4
]}

机构：

[1] Thaksin Univ TSU, Fac Sci, Dept Math & Stat, Phat Tha Lung, Thailand

[2] KMUTT, Fac Sci, Dept Math, Bangkok 10140, Thailand

[3] Gyeongsang Natl Univ, Dept Math Educ, Chinju 660701, South Korea

[4] Gyeongsang Natl Univ, RINS, Chinju 660701, South Korea

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2013年 / 57卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

Hybrid projection method; Inverse-strongly monotone operator; Variational inequality; Equilibrium problem; Relatively quasi-nonexpansive mapping; Maximal monotone operator; FIXED-POINT PROBLEMS; WEAK-CONVERGENCE; GENERALIZED EQUILIBRIUM; ITERATIVE METHOD; HYBRID METHODS; THEOREMS; APPROXIMATION; EXISTENCE;

D O I：

10.1007/s10898-012-0030-1

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：

In this paper, we introduce a new hybrid iterative scheme for finding a common element of the set of zeroes of a maximal monotone operator, the set of fixed points of a relatively quasi-nonexpansive mapping, the sets of solutions of an equilibrium problem and the variational inequality problem in Banach spaces. As applications, we apply our results to obtain strong convergence theorems for a maximal monotone operator and quasi-nonexpansive mappings in Hilbert spaces and we consider a problem of finding a minimizer of a convex function.

引用

页码：1299 / 1318

页数：20

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