We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansive mappings. Next, the strong convergence theorems are obtained, under some appropriate conditions, in uniformly convex and smooth Banach spaces. The main results extend various results existing in the current literature.
Rabian Wangkeeree. Hossein Dehghan. Pakkapon Preechasilp. "Existence and Strong Convergence Theorems for Generalized Mixed Equilibrium Problems of a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces." J. Appl. Math. 2012 (SI03) 1 - 21, 2012. https://doi.org/10.1155/2012/859492