Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems

摘要

The purpose of this paper is to present a new hybrid block iterative scheme by the generalizedf-projection method for finding a common element of the fixed point set for a countable family of uniformlyquasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixedequilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Kleeproperty. Furthermore, we prove that our new iterative scheme converges strongly to a common elementof the aforementioned sets. The results presented in this paper improve and extend important recentresults in the literature.