New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces

<p/> <p>We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Final...

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Main Authors:	Wangkeeree Rabian, Nammanee Kamonrat
Format:	Article
Language:	English
Published:	SpringerOpen 2011-01-01
Series:	Fixed Point Theory and Applications
Online Access:	http://www.fixedpointtheoryandapplications.com/content/2011/671754

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spelling	doaj-b551a0b7fcbc4bc1b599ca7eba3f66112020-11-25T01:00:41ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122011-01-0120111671754New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach SpacesWangkeeree RabianNammanee Kamonrat<p/> <p>We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally, we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive operator. The results presented in this paper mainly improve on the corresponding results reported by many others.</p>http://www.fixedpointtheoryandapplications.com/content/2011/671754
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Wangkeeree Rabian Nammanee Kamonrat
spellingShingle	Wangkeeree Rabian Nammanee Kamonrat New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces Fixed Point Theory and Applications
author_facet	Wangkeeree Rabian Nammanee Kamonrat
author_sort	Wangkeeree Rabian
title	New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces
title_short	New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces
title_full	New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces
title_fullStr	New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces
title_full_unstemmed	New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces
title_sort	new iterative approximation methods for a countable family of nonexpansive mappings in banach spaces
publisher	SpringerOpen
series	Fixed Point Theory and Applications
issn	1687-1820 1687-1812
publishDate	2011-01-01
description	<p/> <p>We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally, we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive operator. The results presented in this paper mainly improve on the corresponding results reported by many others.</p>
url	http://www.fixedpointtheoryandapplications.com/content/2011/671754
work_keys_str_mv	AT wangkeereerabian newiterativeapproximationmethodsforacountablefamilyofnonexpansivemappingsinbanachspaces AT nammaneekamonrat newiterativeapproximationmethodsforacountablefamilyofnonexpansivemappingsinbanachspaces
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New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces

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