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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th-cmuir.6653943832-65702014-08-30T03:24:21Z Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces Cholamjiak P. Suantai S. 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. 2014-08-30T03:24:21Z 2014-08-30T03:24:21Z 2011 Article 8981221 10.1016/j.camwa.2011.03.029 CMAPD http://www.scopus.com/inward/record.url?eid=2-s2.0-79955479760&partnerID=40&md5=a53797416e960ccf676bb533914bc6ec http://cmuir.cmu.ac.th/handle/6653943832/6570 English |
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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 |
Article |
| author |
Cholamjiak P. Suantai S. |
| spellingShingle |
Cholamjiak P. Suantai S. Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces |
| author_facet |
Cholamjiak P. Suantai S. |
| author_sort |
Cholamjiak P. |
| 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 |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-79955479760&partnerID=40&md5=a53797416e960ccf676bb533914bc6ec http://cmuir.cmu.ac.th/handle/6653943832/6570 |
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1681420638606065664 |