A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space

<p>Abstract</p> <p>In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings <inline-formula><graphic file="1687-1812-2011-17-i1.gif"/></inline-formula> and a system of bifuncti...

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Main Authors:	Qu De-ning, Cheng Cao-zong
Format:	Article
Language:	English
Published:	SpringerOpen 2011-01-01
Series:	Fixed Point Theory and Applications
Subjects:	Common solution Equilibrium problem Fixed-point problem Iterative sequence Strong convergence
Online Access:	http://www.fixedpointtheoryandapplications.com/content/2011/1/17

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spelling	doaj-9830b87f567e439c9314dbafb9cd15a62020-11-25T00:03:10ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122011-01-012011117A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach spaceQu De-ningCheng Cao-zong<p>Abstract</p> <p>In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings <inline-formula><graphic file="1687-1812-2011-17-i1.gif"/></inline-formula> and a system of bifunctions <inline-formula><graphic file="1687-1812-2011-17-i2.gif"/></inline-formula> satisfying certain conditions, and the common fixed-point problem (P2) for a family of uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly Hölder continuous mappings <inline-formula><graphic file="1687-1812-2011-17-i3.gif"/></inline-formula> are proposed. A new iterative sequence is constructed by using the generalized projection and hybrid method, and a strong convergence theorem is proved on approximating a common solution of (P1) and (P2) in Banach space.</p> <p><b>2000 MSC: </b>26B25, 40A05</p> http://www.fixedpointtheoryandapplications.com/content/2011/1/17Common solutionEquilibrium problemFixed-point problemIterative sequenceStrong convergence
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Qu De-ning Cheng Cao-zong
spellingShingle	Qu De-ning Cheng Cao-zong A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space Fixed Point Theory and Applications Common solution Equilibrium problem Fixed-point problem Iterative sequence Strong convergence
author_facet	Qu De-ning Cheng Cao-zong
author_sort	Qu De-ning
title	A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space
title_short	A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space
title_full	A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space
title_fullStr	A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space
title_full_unstemmed	A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space
title_sort	strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in banach space
publisher	SpringerOpen
series	Fixed Point Theory and Applications
issn	1687-1820 1687-1812
publishDate	2011-01-01
description	<p>Abstract</p> <p>In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings <inline-formula><graphic file="1687-1812-2011-17-i1.gif"/></inline-formula> and a system of bifunctions <inline-formula><graphic file="1687-1812-2011-17-i2.gif"/></inline-formula> satisfying certain conditions, and the common fixed-point problem (P2) for a family of uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly Hölder continuous mappings <inline-formula><graphic file="1687-1812-2011-17-i3.gif"/></inline-formula> are proposed. A new iterative sequence is constructed by using the generalized projection and hybrid method, and a strong convergence theorem is proved on approximating a common solution of (P1) and (P2) in Banach space.</p> <p><b>2000 MSC: </b>26B25, 40A05</p>
topic	Common solution Equilibrium problem Fixed-point problem Iterative sequence Strong convergence
url	http://www.fixedpointtheoryandapplications.com/content/2011/1/17
work_keys_str_mv	AT qudening astrongconvergencetheoremonsolvingcommonsolutionsforgeneralizedequilibriumproblemsandfixedpointproblemsinbanachspace AT chengcaozong astrongconvergencetheoremonsolvingcommonsolutionsforgeneralizedequilibriumproblemsandfixedpointproblemsinbanachspace AT qudening strongconvergencetheoremonsolvingcommonsolutionsforgeneralizedequilibriumproblemsandfixedpointproblemsinbanachspace AT chengcaozong strongconvergencetheoremonsolvingcommonsolutionsforgeneralizedequilibriumproblemsandfixedpointproblemsinbanachspace
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A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space

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