Iterative method for a finite family of nonexpansive mappings in Hilbert spaces with applications

Abstract

In this paper, we introduce a new iterative method for finding a common element of the set of solutions of a general system of variational inequalities, the set of solutions of a mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove that the studied iterative method converges strongly to a common element of these three sets. Consequently, we apply our main result to the problem of approximating a zero of a finite family of maximal monotone mappings in Hilbert spaces. The theorems presented in this paper, improve and extend the corresponding results of Takahashi and Toyoda [18] and many others.