Semicontinuity of solution set for parametric vector quasi-variational inequality problem

Abstract

In this paper, a key assumption is introduced by virtue of a parametric gap function without the help of the nonlinear scalarization function. Then, by using the key assumption, we establish condition (H$_h$ ) is a sufficient and necessary condition for the lower semicontinuity, the Hausdorff lower semicontinuity, the continuity and Hausdorff continuity of the solution set for parametric vector quasi-variational inequality problem (in short, (QVIP))  in Hausdorff topological vector spaces. The results presented in the paper improve and extend the main results of Li and Chen [Nonlinear Anal. TMA. 70 (2009),  1528-1535].