A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces

A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed po...

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Main Authors: Pongsakorn Sunthrayuth, Poom Kumam
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2011/187052
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spelling doaj-77485454a94548cf9f4215c82d3516062020-11-24T21:03:15ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/187052187052A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach SpacesPongsakorn Sunthrayuth0Poom Kumam1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandWe introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given.http://dx.doi.org/10.1155/2011/187052
collection DOAJ
language English
format Article
sources DOAJ
author Pongsakorn Sunthrayuth
Poom Kumam
spellingShingle Pongsakorn Sunthrayuth
Poom Kumam
A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces
Journal of Applied Mathematics
author_facet Pongsakorn Sunthrayuth
Poom Kumam
author_sort Pongsakorn Sunthrayuth
title A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces
title_short A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces
title_full A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces
title_fullStr A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces
title_full_unstemmed A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces
title_sort new general iterative method for solution of a new general system of variational inclusions for nonexpansive semigroups in banach spaces
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2011-01-01
description We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given.
url http://dx.doi.org/10.1155/2011/187052
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AT poomkumam anewgeneraliterativemethodforsolutionofanewgeneralsystemofvariationalinclusionsfornonexpansivesemigroupsinbanachspaces
AT pongsakornsunthrayuth newgeneraliterativemethodforsolutionofanewgeneralsystemofvariationalinclusionsfornonexpansivesemigroupsinbanachspaces
AT poomkumam newgeneraliterativemethodforsolutionofanewgeneralsystemofvariationalinclusionsfornonexpansivesemigroupsinbanachspaces
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