On the Generalized Mixed Equilibrium Problem in Banach Spaces

The purpose is by using hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problem and the set of common fixed points for a finite family of quasi--nonexpansive mappings in a uniformly smooth and strictly convex Banach space.By utilizing the results for the study of optimization problem,it shows that the results improve and extend the corresponding results announced recently by many others such as Ceng,Takahashi,Qin,et al.