ERGODIC AND FIXED POINT THEOREMS FOR BREGMAN NONEXPANSIVE SEQUENCES AND MAPPINGS IN BANACH SPACES

被引：0

作者：

Rouhani B.D. ^{[1
]}

Khatibzadeh H. ^{[2
]}

Mohebbi V. ^{[1
]}

机构：

[1] Department of Mathematical Sciences, University of Texas at El Paso, El Paso, 79968, TX

[2] Department of Mathematics, University of Zanjan, Zanjan

来源：

Applied Set-Valued Analysis and Optimization | 2022年 / 4卷 / 03期

关键词：

Asymptotic behavior; Asymptotically regular sequence; Bregman nonexpansive sequence; Strong convergence; Weak convergence;

D O I：

10.23952/asvao.4.2022.3.05

中图分类号：

学科分类号：

摘要：

In this paper, we introduce the notion of Bregman nonexpansive sequences and mappings in a Banach space, prove an ergodic theorem and a fixed point theorem, and some weak convergence theorems for such sequences and maps with rather mild assumptions on the Banach space. These results extend our previous results for φ-nonexpansive sequences and give a partial answer to the open problem raised in 1981 by Djafari Rouhani for nonexpansive sequences in a Banach space. ©2022 Applied Set-Valued Analysis and Optimization.

引用

页码：311 / 321

页数：10

共 50 条

[21] Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces
Zegeye, Habtu
Shahzad, Naseer
SCIENTIFIC WORLD JOURNAL, 2014,
[22] Fixed point theorems of mean nonexpansive set-valued mappings in Banach spaces
Chen, Lili
Gao, Lu
Chen, Deyun
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2017, 19 (03) : 2129 - 2143
[23] Fixed point theorem for α-nonexpansive mappings in Banach spaces
Aoyama, Koji
Kohsaka, Fumiaki
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (13) : 4387 - 4391
[24] Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces
Zegeye, H.
Shahzad, N.
ABSTRACT AND APPLIED ANALYSIS, 2014,
[25] Fixed point theorems and demiclosedness principle for mappings of asymptotically nonexpansive type in Banach spaces
Caixia Deng
Jingxin Zhang
Yunan Cui
Fixed Point Theory and Applications, 2012
[26] Fixed point theorems and demiclosedness principle for mappings of asymptotically nonexpansive type in Banach spaces
Deng, Caixia
Zhang, Jingxin
Cui, Yunan
FIXED POINT THEORY AND APPLICATIONS, 2012, : 1 - 11
[27] Fixed point theorems and iterative approximations for monotone nonexpansive mappings in ordered Banach spaces
Song Y.
Kumam P.
Cho Y.J.
Fixed Point Theory and Applications, 2016 (1)
[28] Fixed point theorems of mean nonexpansive set-valued mappings in Banach spaces
Lili Chen
Lu Gao
Deyun Chen
Journal of Fixed Point Theory and Applications, 2017, 19 : 2129 - 2143
[29] Fixed point theorems for nonexpansive maps in Banach spaces
Djebali, Smail
Hammache, Karima
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (10) : 3440 - 3449
[30] Best proximity point theorems for α-nonexpansive mappings in Banach spaces
Kong, Dezhou
Liu, Lishan
Wu, Yonghong
FIXED POINT THEORY AND APPLICATIONS, 2015,

← 1 2 3 4 5 →