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

被引：14

作者：

Takahashi, Wataru ^{[2
]}

Yao, Jen-Chih ^{[1
]}

机构：

[1] Kaohsiung Med Univ, Ctr Gen Educ, Kaohsiung 80707, Taiwan

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

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2011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; VISCOSITY APPROXIMATION METHODS; FIXED-POINTS; ACCRETIVE-OPERATORS; NONLINEAR OPERATORS; RESOLVENTS; FAMILIES;

D O I：

10.11650/twjm/1500406277

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our purpose in this paper is first to prove a weak convergence theorem by Mann's iteration for positively homogeneous nonexpansive mappings in a Banach space. Further, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong convergence theorem for such mappings. From two results, we obtain weak and strong convergence theorems for linear contractive mappings in a Banach space. These results are new even if the mappings are linear and contractive.

引用

页码：961 / 980

页数：20

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