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

<p/> <p>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 p...

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Autores principales:	Takahashi Wataru, Kohsaka Fumiaki
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2007
Materias:	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/7945392063ea466ea4e3b91aa15b5dd4
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spelling	oai:doaj.org-article:7945392063ea466ea4e3b91aa15b5dd42021-12-02T11:34:32ZBlock Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces1687-18201687-1812https://doaj.org/article/7945392063ea466ea4e3b91aa15b5dd42007-01-01T00:00:00Zhttp://www.fixedpointtheoryandapplications.com/content/2007/021972https://doaj.org/toc/1687-1820https://doaj.org/toc/1687-1812<p/> <p>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.</p> Takahashi WataruKohsaka FumiakiSpringerOpenarticleApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2007, Iss 1, p 021972 (2007)
institution	DOAJ
collection	DOAJ
language	EN
topic	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Takahashi Wataru Kohsaka Fumiaki Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
description	<p/> <p>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.</p>
format	article
author	Takahashi Wataru Kohsaka Fumiaki
author_facet	Takahashi Wataru Kohsaka Fumiaki
author_sort	Takahashi Wataru
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
publishDate	2007
url	https://doaj.org/article/7945392063ea466ea4e3b91aa15b5dd4
work_keys_str_mv	AT takahashiwataru blockiterativemethodsforafinitefamilyofrelativelynonexpansivemappingsinbanachspaces AT kohsakafumiaki blockiterativemethodsforafinitefamilyofrelativelynonexpansivemappingsinbanachspaces
_version_	1718395826940674048

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

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