Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces

In this paper, a key assumption similar to that of Li and Chen is introduced by virtue of a gap function for a class of parametric set‐valued weak vector variational inequalities in Banach spaces. By using this key assumption, sufficient and necessary conditions of the continuity and Hausdorff continuity of the solution set mapping for such parametric set‐valued weak vector variational inequalities are given in Banach spaces when the image space is infinite dimensional. The results presented in this paper generalize and improve some main results of Li and Chen.