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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th-cmuir.6653943832-65352014-08-30T03:24:19Z A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces Cholamjiak P. Suantai S. 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. 2014-08-30T03:24:19Z 2014-08-30T03:24:19Z 2011 Article in Press 9255001 10.1007/s10898-011-9743-9 JGOPE http://www.scopus.com/inward/record.url?eid=2-s2.0-79959257516&partnerID=40&md5=e99865b2e73c101c553d9d6741ba8759 http://cmuir.cmu.ac.th/handle/6653943832/6535 English |
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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. |
| format |
Article |
| author |
Cholamjiak P. Suantai S. |
| spellingShingle |
Cholamjiak P. Suantai S. A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces |
| author_facet |
Cholamjiak P. Suantai S. |
| author_sort |
Cholamjiak P. |
| title |
A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces |
| title_short |
A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces |
| title_full |
A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces |
| title_fullStr |
A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces |
| title_full_unstemmed |
A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces |
| title_sort |
hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in banach spaces |
| publishDate |
2014 |
| url |
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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