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

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.