Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict Pseudocontractions

Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict Pseudocontractions

We modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive...

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Main Authors: Qian-Fen Gong, Dao-Jun Wen
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/381592
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spelling doaj-fd7102d0927c4906a6a48c1ccccb0e2c2020-11-24T22:39:19ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/381592381592Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict PseudocontractionsQian-Fen Gong0Dao-Jun Wen1College of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing 400067, ChinaCollege of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaWe modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.http://dx.doi.org/10.1155/2014/381592
collection DOAJ
language English
format Article
sources DOAJ
author Qian-Fen Gong
Dao-Jun Wen
spellingShingle Qian-Fen Gong
Dao-Jun Wen
Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict Pseudocontractions
Journal of Applied Mathematics
author_facet Qian-Fen Gong
Dao-Jun Wen
author_sort Qian-Fen Gong
title Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict Pseudocontractions
title_short Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict Pseudocontractions
title_full Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict Pseudocontractions
title_fullStr Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict Pseudocontractions
title_full_unstemmed Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with k-Strict Pseudocontractions
title_sort further investigation on the relaxed hybrid steepest-descent methods for variational inequalities with k-strict pseudocontractions
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description We modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.
url http://dx.doi.org/10.1155/2014/381592
work_keys_str_mv AT qianfengong furtherinvestigationontherelaxedhybridsteepestdescentmethodsforvariationalinequalitieswithkstrictpseudocontractions
AT daojunwen furtherinvestigationontherelaxedhybridsteepestdescentmethodsforvariationalinequalitieswithkstrictpseudocontractions
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