Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces

Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces

We prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a sol...

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Main Authors: H. Zegeye, N. Shahzad
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/584395
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spelling doaj-4d7d5079314e43df9ea8715f4710ac3b2020-11-24T22:07:40ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/584395584395Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach SpacesH. Zegeye0N. Shahzad1Department of Mathematics, University of Botswana, Private, Bag 00704, Gaborone, BotswanaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a solution of a finite family of convex feasibility problems in reflexive real Banach spaces. Our theorems complement some recent results that have been proved for this important class of nonlinear mappings.http://dx.doi.org/10.1155/2014/584395
collection DOAJ
language English
format Article
sources DOAJ
author H. Zegeye
N. Shahzad
spellingShingle H. Zegeye
N. Shahzad
Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces
Abstract and Applied Analysis
author_facet H. Zegeye
N. Shahzad
author_sort H. Zegeye
title Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces
title_short Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces
title_full Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces
title_fullStr Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces
title_full_unstemmed Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces
title_sort convergence theorems for right bregman strongly nonexpansive mappings in reflexive banach spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a solution of a finite family of convex feasibility problems in reflexive real Banach spaces. Our theorems complement some recent results that have been proved for this important class of nonlinear mappings.
url http://dx.doi.org/10.1155/2014/584395
work_keys_str_mv AT hzegeye convergencetheoremsforrightbregmanstronglynonexpansivemappingsinreflexivebanachspaces
AT nshahzad convergencetheoremsforrightbregmanstronglynonexpansivemappingsinreflexivebanachspaces
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