Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings

Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings

We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain...

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Main Author: Jong Soo Jung
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2009/573156
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spelling doaj-4a845b59aa434688badbf6749328f3fa2020-11-24T22:54:24ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/573156573156Strong Convergence of Viscosity Iteration Methods for Nonexpansive MappingsJong Soo Jung0Department of Mathematics, Dong-A University, Busan 604-714, South KoreaWe propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative scheme to a solution of a ceratin variational inequality is established.http://dx.doi.org/10.1155/2009/573156
collection DOAJ
language English
format Article
sources DOAJ
author Jong Soo Jung
spellingShingle Jong Soo Jung
Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
Abstract and Applied Analysis
author_facet Jong Soo Jung
author_sort Jong Soo Jung
title Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
title_short Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
title_full Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
title_fullStr Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
title_full_unstemmed Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
title_sort strong convergence of viscosity iteration methods for nonexpansive mappings
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2009-01-01
description We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative scheme to a solution of a ceratin variational inequality is established.
url http://dx.doi.org/10.1155/2009/573156
work_keys_str_mv AT jongsoojung strongconvergenceofviscosityiterationmethodsfornonexpansivemappings
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