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

In this paper, we study the solution stability of parametric weak Vector Variational Inequalities with set‐valued and single‐valued mappings, respectively. We obtain the lower semicontinuity of the solution mapping for the parametric set‐valued weak Vector Variational Inequality with strictly C‐pseudomapping in reflexive Banach spaces. Moreover, under some requirements that the mapping satisfies the degree conditions, we establish the lower semicontinuity of the solution mapping for a parametric single‐valued weak Vector Variational Inequality in reflexive Banach spaces, by using the degree‐theoretic approach. The results presented in this paper improve and extend some known results due to Kien and Yao (2008) and Wong (2010).