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

共 50 条

[11] STRONG CONVERGENCE THEOREMS FOR TWO GENERIC 2-GENERALIZED NONSPREADING MAPPINGS IN BANACH SPACES
Takahashi, Wataru
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2020, 21 (02) : 275 - 294
[12] WEAK CONVERGENCE THEOREMS FOR NONCOMMUTATIVE GENERIC 2-GENERALIZED NONSPREADING MAPPINGS IN BANACH SPACES
Lin, Chien-Nan
Takahashi, Wataru
Wen, Ching-Feng
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2020, 21 (06) : 1349 - 1366
[13] ATTRACTIVE POINT AND WEAK CONVERGENCE THEOREMS FOR NEW GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES
Takahashi, Wataru
Wong, Ngai-Ching
Yao, Jen-Chih
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2012, 13 (04) : 745 - 757
[14] Common Attractive Point Approximations for Family of Generic Generalized Bregman Nonspreading Mappings in Banach Spaces
Ali, B.
Haruna, L. Y.
Harbau, M. H.
[J]. AZERBAIJAN JOURNAL OF MATHEMATICS, 2023, 13 (02): : 27 - 50
[15] WEAK AND STRONG CONVERGENCE THEOREMS FOR COMMUTATIVE 2-GENERALIZED NONSPREADING MAPPINGS IN BANACH SPACES
Alsulami, Saud M.
Latif, Abdul
Takahashi, Wataru
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2018, 19 (02) : 345 - 364
[16] WEAK AND STRONG CONVERGENCE THEOREMS FOR COMMUTATIVE GENERIC 2-GENERALIZED NONSPREADING MAPPINGS IN BANACH SPACES
Takahashi, Wataru
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2020, 21 (03) : 715 - 739
[17] Iterative Approximations of Attractive Point of A New Generalized Bregman Nonspreading Mapping in Banach Spaces
Ali, Bashir
Haruna, Lawal Yusuf
[J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2020, 46 (02) : 331 - 354
[18] Iterative Approximations of Attractive Point of A New Generalized Bregman Nonspreading Mapping in Banach Spaces
Bashir Ali
Lawal Yusuf Haruna
[J]. Bulletin of the Iranian Mathematical Society, 2020, 46 : 331 - 354
[19] ATTRACTIVE POINT AND MEAN CONVERGENCE THEOREMS FOR SEMIGROUPS OF MAPPINGS WITHOUT CONTINUITY IN HILBERT SPACES
Takahashi, Wataru
Wong, Ngai-Ching
Yao, Jen-Chih
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2014, 15 (06) : 1087 - 1103
[20] STRONG CONVERGENCE THEOREMS BY HYBRID METHODS FOR GENERIC SKEW 2-GENERALIZED NONSPREADING MAPPINGS IN BANACH SPACES
Takahashi, Wataru
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2019, 20 (11) : 2425 - 2446

← 1 2 3 4 5 →