Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators

Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators

<p/> <p>The purpose of this paper is to introduce and study two modified hybrid proximal-point algorithms for finding a common element of the solution set <it>EP</it> of a generalized equilibrium problem and the set <inline-formula> <graphic file="1687-1812-2010...

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Main Authors: Yao J-C, Shyu DavidS, Ansari QH, Zeng L-C
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Fixed Point Theory and Applications
Online Access:http://www.fixedpointtheoryandapplications.com/content/2010/590278
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spelling doaj-55c1120f166842ce98af125180404b1b2020-11-24T20:49:48ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101590278Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone OperatorsYao J-CShyu DavidSAnsari QHZeng L-C<p/> <p>The purpose of this paper is to introduce and study two modified hybrid proximal-point algorithms for finding a common element of the solution set <it>EP</it> of a generalized equilibrium problem and the set <inline-formula> <graphic file="1687-1812-2010-590278-i1.gif"/></inline-formula> for two maximal monotone operators <inline-formula> <graphic file="1687-1812-2010-590278-i2.gif"/></inline-formula> and <inline-formula> <graphic file="1687-1812-2010-590278-i3.gif"/></inline-formula> defined on a Banach space <inline-formula> <graphic file="1687-1812-2010-590278-i4.gif"/></inline-formula>. Strong and weak convergence theorems for these two modified hybrid proximal-point algorithms are established.</p>http://www.fixedpointtheoryandapplications.com/content/2010/590278
collection DOAJ
language English
format Article
sources DOAJ
author Yao J-C
Shyu DavidS
Ansari QH
Zeng L-C
spellingShingle Yao J-C
Shyu DavidS
Ansari QH
Zeng L-C
Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators
Fixed Point Theory and Applications
author_facet Yao J-C
Shyu DavidS
Ansari QH
Zeng L-C
author_sort Yao J-C
title Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators
title_short Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators
title_full Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators
title_fullStr Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators
title_full_unstemmed Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators
title_sort strong and weak convergence theorems for common solutions of generalized equilibrium problems and zeros of maximal monotone operators
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2010-01-01
description <p/> <p>The purpose of this paper is to introduce and study two modified hybrid proximal-point algorithms for finding a common element of the solution set <it>EP</it> of a generalized equilibrium problem and the set <inline-formula> <graphic file="1687-1812-2010-590278-i1.gif"/></inline-formula> for two maximal monotone operators <inline-formula> <graphic file="1687-1812-2010-590278-i2.gif"/></inline-formula> and <inline-formula> <graphic file="1687-1812-2010-590278-i3.gif"/></inline-formula> defined on a Banach space <inline-formula> <graphic file="1687-1812-2010-590278-i4.gif"/></inline-formula>. Strong and weak convergence theorems for these two modified hybrid proximal-point algorithms are established.</p>
url http://www.fixedpointtheoryandapplications.com/content/2010/590278
work_keys_str_mv AT yaojc strongandweakconvergencetheoremsforcommonsolutionsofgeneralizedequilibriumproblemsandzerosofmaximalmonotoneoperators
AT shyudavids strongandweakconvergencetheoremsforcommonsolutionsofgeneralizedequilibriumproblemsandzerosofmaximalmonotoneoperators
AT ansariqh strongandweakconvergencetheoremsforcommonsolutionsofgeneralizedequilibriumproblemsandzerosofmaximalmonotoneoperators
AT zenglc strongandweakconvergencetheoremsforcommonsolutionsofgeneralizedequilibriumproblemsandzerosofmaximalmonotoneoperators
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