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.
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页码：225 / 248
页数：24
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