A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces
We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using the...
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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-s2.0-79959257516&partnerID=40&md5=e99865b2e73c101c553d9d6741ba8759 http://cmuir.cmu.ac.th/handle/6653943832/6535 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using the concept of the Mosco convergence when the family {Tn} satisfies the (*)-condition. The examples of three generated mappings which satisfy the (*)-condition are also given. Using the obtained result, we give some applications concerning the variational inequality problem and the convex minimization problem. © 2011 Springer Science+Business Media, LLC. |
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