Semicontinuity for parametric Minty vector quasivariational inequalities in Hausdorff topological vector spaces

Abstract

This paper is devoted to the semicontinuity of solutions of a parametric generalized Minty vector quasivariational inequality problem with set-valued mappings [(in short (PGMVQVI)] in Hausdorff topological vector spaces, when the mapping and the constraint sets are perturbed by different parameters. The upper (lower) semicontinuity and closedness of the solution set mapping for (PGMVQVI) are established under some appropriate assumptions. The sufficient and necessary conditions of the Hausdorff lower semicontinuity and Hausdorff continuity of the solution set mapping for (PGMVQVI) are also derived without monotonicity. As an application, we discuss the upper semicontinuity for the solution set mapping of a special case of the (PGMVQVI).