A new general system of variational inequalities for convergence theorem and application

Abstract

In this present paper, we propose a modified form of generalized system of variational inequalities and introduce an iterative scheme for finding a common element of the set of fixed points of nonexpansive mapping and the solution set of the proposed problem in the framework of real Hilbert spaces. We prove a strong convergence theorem of the proposed iterative scheme. Applying our main result, we prove strong convergence theorems of the standard constrained convex optimization problem and the split feasibility problem. In support of our main result, a numerical example is also presented.