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 |
| Published: |
Springer Netherlands
2015
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| Subjects: | |
| Online Access: | http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84865141523&origin=inward http://cmuir.cmu.ac.th/handle/6653943832/38637 |
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| Institution: | Chiang Mai University |
| 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 {T n} 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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