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 (Set-Valued Anal. 16:399-412, 2008) and Wong (J. Glob. Optim. 46:435-446, 2010).