A Viscosity Approximation Method for Solving General System of Variational Inequalities, Generalized Mixed Equilibrium Problems and Fixed Point Problems

Abstract

This paper is devoted to introducing a new viscosity approximation method using the implicit midpoint rules for finding a common element in the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a general system of variational inequalities and the set of common fixed points of a finite family of nonexpansive mappings in a symmetric Hilbert space. Then, we prove a strong convergence theorem regarding the proposed iterative scheme under some suitable conditions on the parameters. Finally, we provide two numerical results to show the consistency and accuracy of the scheme. One of them, moreover, compares the behavior of our scheme with the iterative scheme of Ke and Ma (Fixed Point Theory Appl 190, 2015).