On the solution semicontinuity to a parametric generalized vector quasivariational inequality

In this paper, the semicontinuities of the solution set map are investigated for a parametric generalized vector quasivariational inequality in locally convex Hausdorff topological vector spaces. The upper semicontinuity and closedness of the solution set map are obtained. A parametric gap function is proposed by using a nonlinear scalarization function. By virtue of the parametric gap function and a key assumption, the Hausdorff lower semicontinuity of the solution set map is established.