Attractive Point and Mean Convergence Theorems for New Generalized Nonspreading Mappings in Banach Spaces

被引：17

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：

INFINITE PRODUCTS OF OPERATORS AND THEIR APPLICATIONS | 2015年 / 636卷

关键词：

Attractive point; Banach limit; Banach space; fixed point; generalized nonspreading mapping; mean convergence; PROXIMAL-TYPE ALGORITHM; MAXIMAL MONOTONE-OPERATORS; NONLINEAR ERGODIC THEOREM; FIXED-POINT; NONEXPANSIVE-MAPPINGS; HILBERT-SPACES; HYBRID MAPPINGS; ASYMPTOTIC-BEHAVIOR; WEAK; APPROXIMATION;

D O I：

10.1090/conm/636/12740

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 first introduce a new class of nonlinear mappings in a Banach space. Then we prove an attractive point theorem for such mappings in a Banach space. Furthermore, we prove a mean convergence theorem of Baillon's type and a weak convergence theorem of Mann's type for such nonlinear mappings in a Banach space. These results generalize attractive point, mean convergence and weak convergence theorems proved by Lin and Takahashi [28] and Kocourek, Takahashi and Yao [23] in a Banach space.

引用

页码：225 / 248

页数：24

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