A New Hybrid Algorithm for a Pair of Quasi-ϕ-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces

Abstract EN

The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi-ϕ-asymptotically nonexpansive mappings.

Under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with Kadec-Klee property.

The results presented in the paper improve and extend some recent results.