Existence of solutions for mixed variational inequalities with perturbation in Banach spaces

Abstract

This paper is mainly devoted to the existence of solutions of generalized mixed variational inequalities (GMVI for short) with perturbation in reflexive Banach spaces. When the constraint set is weakly compact, we deduce two existence theorems for GMVI. Based on these two existence theorems, when the constraint set is unbounded, we obtain some existence theorems for GMVI perturbed by a nonlinear continuous mapping in finite dimensional spaces (resp. a multiplication of a scalar and a vector taken from the interior of the barrier cone of the constraint set in reflexive Banach spaces). The main results presented in this paper generalize some corresponding known results.