Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces

Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mapping...

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Main Authors:	Fumiaki Kohsaka, Wataru Takahashi
Format:	Article
Language:	English
Published:	SpringerOpen 2007-01-01
Series:	Fixed Point Theory and Applications
Online Access:	http://dx.doi.org/10.1155/2007/21972

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spelling	doaj-61498684c99a400b83182fc23863ea3b2020-11-24T22:20:05ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122007-01-01200710.1155/2007/21972Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach SpacesFumiaki KohsakaWataru TakahashiUsing the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.http://dx.doi.org/10.1155/2007/21972
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Fumiaki Kohsaka Wataru Takahashi
spellingShingle	Fumiaki Kohsaka Wataru Takahashi Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces Fixed Point Theory and Applications
author_facet	Fumiaki Kohsaka Wataru Takahashi
author_sort	Fumiaki Kohsaka
title	Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
title_short	Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
title_full	Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
title_fullStr	Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
title_full_unstemmed	Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
title_sort	block iterative methods for a finite family of relatively nonexpansive mappings in banach spaces
publisher	SpringerOpen
series	Fixed Point Theory and Applications
issn	1687-1820 1687-1812
publishDate	2007-01-01
description	Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.
url	http://dx.doi.org/10.1155/2007/21972
work_keys_str_mv	AT fumiakikohsaka blockiterativemethodsforafinitefamilyofrelativelynonexpansivemappingsinbanachspaces AT watarutakahashi blockiterativemethodsforafinitefamilyofrelativelynonexpansivemappingsinbanachspaces
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Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces

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