Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces

Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces

We first introduce a new class of mappings called Bregman asymptotic pointwise nonexpansive mappings and investigate the existence and the approximation of fixed points of such mappings defined on a nonempty, bounded, closed, and convex subset C of a real Banach space E. Without using the original O...

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Main Authors: Chin-Tzong Pang, Eskandar Naraghirad
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/316813
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spelling doaj-d7301ac359514dd19efa8419b5f1b3182020-11-24T22:37:42ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/316813316813Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach SpacesChin-Tzong Pang0Eskandar Naraghirad1Department of Information Management, Yuan Ze University, Chung-Li 32003, TaiwanDepartment of Mathematics, Yasouj University, Yasouj 75918, IranWe first introduce a new class of mappings called Bregman asymptotic pointwise nonexpansive mappings and investigate the existence and the approximation of fixed points of such mappings defined on a nonempty, bounded, closed, and convex subset C of a real Banach space E. Without using the original Opial property of a Banach space E, we prove weak convergence theorems for the sequences produced by generalized Mann and Ishikawa iteration processes for Bregman asymptotic pointwise nonexpansive mappings in a reflexive Banach space E. Our results are applicable in the function spaces Lp, where 1<p<∞ is a real number.http://dx.doi.org/10.1155/2013/316813
collection DOAJ
language English
format Article
sources DOAJ
author Chin-Tzong Pang
Eskandar Naraghirad
spellingShingle Chin-Tzong Pang
Eskandar Naraghirad
Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces
Abstract and Applied Analysis
author_facet Chin-Tzong Pang
Eskandar Naraghirad
author_sort Chin-Tzong Pang
title Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces
title_short Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces
title_full Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces
title_fullStr Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces
title_full_unstemmed Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces
title_sort bregman asymptotic pointwise nonexpansive mappings in banach spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description We first introduce a new class of mappings called Bregman asymptotic pointwise nonexpansive mappings and investigate the existence and the approximation of fixed points of such mappings defined on a nonempty, bounded, closed, and convex subset C of a real Banach space E. Without using the original Opial property of a Banach space E, we prove weak convergence theorems for the sequences produced by generalized Mann and Ishikawa iteration processes for Bregman asymptotic pointwise nonexpansive mappings in a reflexive Banach space E. Our results are applicable in the function spaces Lp, where 1<p<∞ is a real number.
url http://dx.doi.org/10.1155/2013/316813
work_keys_str_mv AT chintzongpang bregmanasymptoticpointwisenonexpansivemappingsinbanachspaces
AT eskandarnaraghirad bregmanasymptoticpointwisenonexpansivemappingsinbanachspaces
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