Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems

Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences genera...

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Main Authors: Kamonrat Sombut, Somyot Plubtieng
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/430409
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spelling doaj-750ce9d768f2421181dfac800cebfb542020-11-24T21:45:46ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/430409430409Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium ProblemsKamonrat Sombut0Somyot Plubtieng1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandThe purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.http://dx.doi.org/10.1155/2013/430409
collection DOAJ
language English
format Article
sources DOAJ
author Kamonrat Sombut
Somyot Plubtieng
spellingShingle Kamonrat Sombut
Somyot Plubtieng
Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems
Abstract and Applied Analysis
author_facet Kamonrat Sombut
Somyot Plubtieng
author_sort Kamonrat Sombut
title Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems
title_short Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems
title_full Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems
title_fullStr Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems
title_full_unstemmed Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems
title_sort weak convergence theorem for finding fixed points and solution of split feasibility and systems of equilibrium problems
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.
url http://dx.doi.org/10.1155/2013/430409
work_keys_str_mv AT kamonratsombut weakconvergencetheoremforfindingfixedpointsandsolutionofsplitfeasibilityandsystemsofequilibriumproblems
AT somyotplubtieng weakconvergencetheoremforfindingfixedpointsandsolutionofsplitfeasibilityandsystemsofequilibriumproblems
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