A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings

A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings

We consider a hybrid projection algorithm basing on the shrinking projection method for two families of relatively weak quasi-nonexpansive mappings. We establish strong convergence theorems for approximating the common fixed point of the set of the common fixed points of such two families and the se...

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Main Authors: Rabian Wangkeeree, Uthai Kamraksa
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Journal of Inequalities and Applications
Online Access:http://dx.doi.org/10.1155/2010/724851
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spelling doaj-1a42ed147b0b4bca8ec5c80d30f9fe3d2020-11-25T00:23:16ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-01201010.1155/2010/724851A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive MappingsRabian WangkeereeUthai KamraksaWe consider a hybrid projection algorithm basing on the shrinking projection method for two families of relatively weak quasi-nonexpansive mappings. We establish strong convergence theorems for approximating the common fixed point of the set of the common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. At the end of the paper, we apply our results to consider the problem of finding a solution of the complementarity problem. Our results improve and extend the corresponding results announced by recent results. http://dx.doi.org/10.1155/2010/724851
collection DOAJ
language English
format Article
sources DOAJ
author Rabian Wangkeeree
Uthai Kamraksa
spellingShingle Rabian Wangkeeree
Uthai Kamraksa
A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings
Journal of Inequalities and Applications
author_facet Rabian Wangkeeree
Uthai Kamraksa
author_sort Rabian Wangkeeree
title A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings
title_short A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings
title_full A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings
title_fullStr A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings
title_full_unstemmed A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings
title_sort hybrid iterative scheme for variational inequality problems for finite families of relatively weak quasi-nonexpansive mappings
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 2010-01-01
description We consider a hybrid projection algorithm basing on the shrinking projection method for two families of relatively weak quasi-nonexpansive mappings. We establish strong convergence theorems for approximating the common fixed point of the set of the common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. At the end of the paper, we apply our results to consider the problem of finding a solution of the complementarity problem. Our results improve and extend the corresponding results announced by recent results.
url http://dx.doi.org/10.1155/2010/724851
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