Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi- ϕ -Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces

Abstract

The main purpose of this paper is by using a 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 problems, and the set of common fixed points for a infinite family of total quasi-$\varphi$-asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors.