Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces

We prove the existence of a solution of the mixed equilibrium problem (MEP) by using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solutions set of a mixed equilibrium problem and the fixed points set of...

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Main Authors:	Prasit Cholamjiak, Suthep Suantai
Format:	Journal
Published:	2018
Subjects:	Computer Science Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79955479760&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49888
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-498882018-09-04T04:24:44Z Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces Prasit Cholamjiak Suthep Suantai Computer Science Mathematics We prove the existence of a solution of the mixed equilibrium problem (MEP) by using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solutions set of a mixed equilibrium problem and the fixed points set of a countable family of nonexpansive mappings in the frameworks of Banach spaces. By using a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solutions set of MEP and common fixed points set of nonexpansive mappings. Moreover, some applications concerning the equilibrium and the convex minimization problems are obtained. © 2011 Elsevier Ltd. All rights reserved. 2018-09-04T04:19:46Z 2018-09-04T04:19:46Z 2011-05-01 Journal 08981221 2-s2.0-79955479760 10.1016/j.camwa.2011.03.029 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79955479760&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49888
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Computer Science Mathematics
spellingShingle	Computer Science Mathematics Prasit Cholamjiak Suthep Suantai Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces
description	We prove the existence of a solution of the mixed equilibrium problem (MEP) by using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solutions set of a mixed equilibrium problem and the fixed points set of a countable family of nonexpansive mappings in the frameworks of Banach spaces. By using a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solutions set of MEP and common fixed points set of nonexpansive mappings. Moreover, some applications concerning the equilibrium and the convex minimization problems are obtained. © 2011 Elsevier Ltd. All rights reserved.
format	Journal
author	Prasit Cholamjiak Suthep Suantai
author_facet	Prasit Cholamjiak Suthep Suantai
author_sort	Prasit Cholamjiak
title	Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces
title_short	Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces
title_full	Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces
title_fullStr	Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces
title_full_unstemmed	Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces
title_sort	existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in banach spaces
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79955479760&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49888
_version_	1681423491077767168

Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces

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