Convergence Analysis for Family of Weak Relatively Nonexpansive Mappings and System of Equilibrium Problems

In this paper, we construct a new iterative scheme by hybrid methods to approximate a common element of the fixed points set of an infinite family of weak relatively nonexpansive mappings and the solutions set of a system of equilibrium problems in a a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f-projection operator. Then, we prove strong convergence of the scheme to a common element of the two sets. We give applications of our results in a Banach space. Our results extend many known recent results in the literature.