Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces

Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces

We study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with nonself-mappings in Hilbert and Banach spaces. We prove strong and weak convergences for weakly contractive and nonexpansive maps, respectively. We also establish the stabili...

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Main Authors: Yakov Alber, Simeon Reich, Jen-Chih Yao
Format: Article
Language:English
Published: Hindawi Limited 2003-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/S1085337503203018
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spelling doaj-0a53e69827a44a3596d1dca8fb8f432b2020-11-24T22:07:28ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092003-01-012003419321610.1155/S1085337503203018Iterative methods for solving fixed-point problems with nonself-mappings in Banach spacesYakov Alber0Simeon Reich1Jen-Chih Yao2Department of Mathematics, The Technion - Israel Institute of Technology, Haifa 32000, IsraelDepartment of Mathematics, The Technion - Israel Institute of Technology, Haifa 32000, IsraelDepartment of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804 , TaiwanWe study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with nonself-mappings in Hilbert and Banach spaces. We prove strong and weak convergences for weakly contractive and nonexpansive maps, respectively. We also establish the stability of these methods with respect to perturbations of the operators and the constraint sets.http://dx.doi.org/10.1155/S1085337503203018
collection DOAJ
language English
format Article
sources DOAJ
author Yakov Alber
Simeon Reich
Jen-Chih Yao
spellingShingle Yakov Alber
Simeon Reich
Jen-Chih Yao
Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces
Abstract and Applied Analysis
author_facet Yakov Alber
Simeon Reich
Jen-Chih Yao
author_sort Yakov Alber
title Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces
title_short Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces
title_full Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces
title_fullStr Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces
title_full_unstemmed Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces
title_sort iterative methods for solving fixed-point problems with nonself-mappings in banach spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2003-01-01
description We study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with nonself-mappings in Hilbert and Banach spaces. We prove strong and weak convergences for weakly contractive and nonexpansive maps, respectively. We also establish the stability of these methods with respect to perturbations of the operators and the constraint sets.
url http://dx.doi.org/10.1155/S1085337503203018
work_keys_str_mv AT yakovalber iterativemethodsforsolvingfixedpointproblemswithnonselfmappingsinbanachspaces
AT simeonreich iterativemethodsforsolvingfixedpointproblemswithnonselfmappingsinbanachspaces
AT jenchihyao iterativemethodsforsolvingfixedpointproblemswithnonselfmappingsinbanachspaces
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