WEAK AND STRONG CONVERGENCE THEOREMS FOR COMMUTATIVE FAMILIES OF POSITIVELY HOMOGENEOUS NONEXPANSIVE MAPPINGS IN BANACH SPACES

被引：0

作者：

Takahashi, Wataru ^{[1
,2
]}

Wong, Ngai-Ching ^{[1
,3
]}

Yao, Jen-Chih ^{[3
,4
]}

机构：

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

[2] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan

[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80702, Taiwan

[4] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2014年 / 15卷 / 03期

基金：

日本学术振兴会;

关键词：

Banach space; nonexpansive mapping; fixed point; generalized nonexpansive mapping; hybrid method; Mann's iteration; MAXIMAL MONOTONE-OPERATORS; FIXED-POINT THEOREMS; VISCOSITY APPROXIMATION METHODS; NONLINEAR ERGODIC-THEOREMS; PROXIMAL-TYPE ALGORITHM; ACCRETIVE-OPERATORS; RESOLVENTS; RETRACTIONS; SEMIGROUPS; EXISTENCE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first prove a weak convergence theorem by Mann's iteration for a commutative family of positively homogeneous nonexpansive mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong convergence theorem for such a family of the mappings. These results are new even if the mappings are linear and contractive.

引用

页码：557 / 572

页数：16

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