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

[41] WEAK CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS AND NONEXPANSIVE MAPPINGS AND NONSPREADING MAPPINGS IN HILBERT SPACES
Jiang, Li
Su, Yongfu
[J]. COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 27 (03): : 505 - 512
[42] Convergence theorems of a new iteration for asymptotically nonexpansive mappings in Banach spaces
Jong Kyu Kim
Won Hee Lim
[J]. Journal of Inequalities and Applications, 2013 (1)
[43] Attractive points and convergence theorems for normally generalized hybrid mappings in CAT(0) spaces
Kaewkhao, A.
Inthakon, W.
Kunwai, K.
[J]. FIXED POINT THEORY AND APPLICATIONS, 2015,
[44] Attractive points and convergence theorems for normally generalized hybrid mappings in CAT(0) spaces
A Kaewkhao
W Inthakon
K Kunwai
[J]. Fixed Point Theory and Applications, 2015
[45] FIXED POINT THEOREMS AND WEAK CONVERGENCE THEOREMS FOR GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES
Kocourek, Pavel
Takahashi, Wataru
Yao, Jen-Chih
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2010, 14 (06): : 2497 - 2511
[46] Fixed point theorems and Δ-convergence theorems for generalized hybrid mappings on CAT(0) spaces
Lai-Jiu Lin
Chih-Sheng Chuang
Zenn-Tsun Yu
[J]. Fixed Point Theory and Applications, 2011
[47] Fixed point theorems and Δ-convergence theorems for generalized hybrid mappings on CAT(0) spaces
Lin, Lai-Jiu
Chuang, Chih-Sheng
Yu, Zenn-Tsun
[J]. FIXED POINT THEORY AND APPLICATIONS, 2011, : 1 - 15
[48] Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
Abkar, A.
Eslamian, M.
[J]. FIXED POINT THEORY AND APPLICATIONS, 2010,
[49] Some fixed point theorems for generalized enriched nonexpansive mappings in Banach spaces
Rahul Shukla
Rekha Panicker
[J]. Rendiconti del Circolo Matematico di Palermo Series 2, 2023, 72 : 1087 - 1101
[50] COMMON FIXED POINT THEOREMS FOR MULTIVALUED GENERALIZED (a,β)-NONEXPANSIVE MAPPINGS IN BANACH SPACES
Wiriyapongsanon, Atit
Inthakon, Warunun
Phudolsitthiphat, Narawadee
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2023, 24 (11) : 2513 - 2529

← 1 2 3 4 5 →