Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces


Authors

Chakkrid Klin-eam - Department of Mathematics, Faculty of Science, Naresuan University, , Thailand., Phitsanulok, 65000, Thailand. - Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, 65000, Thailand. Prondanai Kaskasem - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand. Suthep Suantai - Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand.


Abstract

We introduce a hybrid method for finding a common element of the set of solutions of an equilibrium problem defined on the dual space of a Banach space and the set of common fixed points of a family of generalized nonexpansive mappings and prove strong convergence theorems by using the new hybrid method. Using our main results, we obtain some new strong convergence theorems for finding a solution of an equilibrium problem and a fixed point of a family of generalized nonexpansive mappings in a Banach space.


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