A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces
We introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong...
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Series: | Fixed Point Theory and Applications |
Online Access: | http://dx.doi.org/10.1155/2009/369215 |
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doaj-f2bad3c441444ec2a6e785c9eb7e99802020-11-25T00:21:45ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122009-01-01200910.1155/2009/369215A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert SpacesRabian WangkeereeUthai KamraksaWe introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. As applications, at the end of the paper we utilize our results to study the problem of finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings and the set of fixed points of a finite family of k-strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho (2008). http://dx.doi.org/10.1155/2009/369215 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rabian Wangkeeree Uthai Kamraksa |
spellingShingle |
Rabian Wangkeeree Uthai Kamraksa A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces Fixed Point Theory and Applications |
author_facet |
Rabian Wangkeeree Uthai Kamraksa |
author_sort |
Rabian Wangkeeree |
title |
A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces |
title_short |
A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces |
title_full |
A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces |
title_fullStr |
A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces |
title_full_unstemmed |
A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces |
title_sort |
general iterative method for solving the variational inequality problem and fixed point problem of an infinite family of nonexpansive mappings in hilbert spaces |
publisher |
SpringerOpen |
series |
Fixed Point Theory and Applications |
issn |
1687-1820 1687-1812 |
publishDate |
2009-01-01 |
description |
We introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. As applications, at the end of the paper we utilize our results to study the problem of finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings and the set of fixed points of a finite family of k-strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho (2008). |
url |
http://dx.doi.org/10.1155/2009/369215 |
work_keys_str_mv |
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1716181993612378112 |