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.
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页码：557 / 572
页数：16
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