A New Modified Block Iterative Algorithm for a System of Equilibrium Problems and a Fixed Point Set of Uniformly Quasi-φ-Asymptotically Nonexpansive Mappings

Abstract

In this paper, we construct a new modified block hybrid projection algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-φ-asymptotically nonexpansive mappings, the set of the variational inequality for an inverse-strongly monotone operator, the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequences generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature.