A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces
<p/> <p>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 cond...
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2009-01-01
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doaj-bb5fad557d7c400e9b1e99f90ec1afd22020-11-24T21:25:19ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122009-01-0120091369215A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert SpacesWangkeeree RabianKamraksa Uthai<p/> <p>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 <inline-formula> <graphic file="1687-1812-2009-369215-i1.gif"/></inline-formula>-strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho (2008).</p>http://www.fixedpointtheoryandapplications.com/content/2009/369215 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Wangkeeree Rabian Kamraksa Uthai |
spellingShingle |
Wangkeeree Rabian Kamraksa Uthai 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 |
Wangkeeree Rabian Kamraksa Uthai |
author_sort |
Wangkeeree Rabian |
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 |
<p/> <p>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 <inline-formula> <graphic file="1687-1812-2009-369215-i1.gif"/></inline-formula>-strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho (2008).</p> |
url |
http://www.fixedpointtheoryandapplications.com/content/2009/369215 |
work_keys_str_mv |
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1716720086611394560 |