Strong Convergence Theorems for Family of Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems

Abstract EN

We introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings, the set of common solutions to a system of generalized mixed equilibrium problems, and the set of solutions to a variational inequality problem in a real Hilbert space.

We then prove strong convergence of the scheme to a common element of the three sets.

We give some applications of our results.

Our results extend important recent results.