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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2014
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| Online Access: | 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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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | 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. |
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