Existence of a solution for generalized vector variational inequalities

It is known that vector variational inequality models arise from vector optimization and vector traffic equilibria. In this paper, existence results of a solution for a generalized vector pre-variational inequality and a generalized vector pre-quasi-variational inequality are established. The main condition used is that the underlying vector-valued function is assumed to be cone-quasi-convex. The main techniques employed are a nonlinear scalarization and fixed point theorems.