SOLVABILITY OF A SYSTEM OF GENERALIZED NONLINEAR MIXED VARIATIONAL-LIKE INEQUALITIES

Abstract

In this paper, we introduce and study a new system of generalized nonlinear mixed variational-like inequalities. By applying the Lemma of Ky Fan, we prove an exis- tence theorem of solution of auxiliary problem for the system of generalized nonlinear mixed variational-like inequalities. By virtue of this existence result, we suggest and analyze an iterative method to compute the approximate solutions of the system of generalized nonlinear mixed variational-like inequalities and establish the convergence criteria of the iterative method. The results presented in this paper improve, extend and unify many known results in this area.