Strong convergence theorems by hybrid methods for nonexpansive mappings with equilibrium problems in Banach spaces

被引：1

作者：

Takahashi, Wataru ^{[1
,2
]}

Yao, Jen-Chih ^{[2
]}

机构：

[1] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo, Japan

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

来源：

ADVANCES IN MATHEMATICAL ECONOMICS, VOL 14 | 2011年 / 14卷

基金：

日本学术振兴会;

关键词：

Nonexpansive mapping; fixed point; hybrid method; Mosco convergence; equilibrium problem; projection; MAXIMAL MONOTONE-OPERATORS; FIXED-POINT THEOREMS; NONLINEAR MAPPINGS; WEAK; APPROXIMATION; RESOLVENTS; FAMILY;

D O I：

10.1007/978-4-431-53883-7_9

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

Our purpose in this paper is to prove strong convergence theorems by hybrid methods for nonexpansive mappings in a Banach space under appropriate conditions. We first prove a strong convergence theorem by the shrinking projection method for semi-positively homogeneous nonexpansive mappings with an equilibrium problem in a Banach space. Next, we obtain another strong convergence theorem by the monotone hybrid method for semi-positively homogeneous nonexpansive mappings with an equilibrium problem in a Banach space. These theorems are proved by using the concept of set convergence.

引用

页码：197 / +

页数：5

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