Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for...

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Main Authors: Watcharaporn Cholamjiak, Suthep Suantai
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2009/297565
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spelling doaj-1dc8972657d146c28a9e4c8a9ab32e112020-11-24T22:52:38ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/297565297565Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive MappingsWatcharaporn Cholamjiak0Suthep Suantai1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandWe prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).http://dx.doi.org/10.1155/2009/297565
collection DOAJ
language English
format Article
sources DOAJ
author Watcharaporn Cholamjiak
Suthep Suantai
spellingShingle Watcharaporn Cholamjiak
Suthep Suantai
Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings
Abstract and Applied Analysis
author_facet Watcharaporn Cholamjiak
Suthep Suantai
author_sort Watcharaporn Cholamjiak
title Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings
title_short Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings
title_full Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings
title_fullStr Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings
title_full_unstemmed Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings
title_sort monotone hybrid projection algorithms for an infinitely countable family of lipschitz generalized asymptotically quasi-nonexpansive mappings
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2009-01-01
description We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).
url http://dx.doi.org/10.1155/2009/297565
work_keys_str_mv AT watcharaporncholamjiak monotonehybridprojectionalgorithmsforaninfinitelycountablefamilyoflipschitzgeneralizedasymptoticallyquasinonexpansivemappings
AT suthepsuantai monotonehybridprojectionalgorithmsforaninfinitelycountablefamilyoflipschitzgeneralizedasymptoticallyquasinonexpansivemappings
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