A topological approach for vector quasi-variational inequalities with set-valued functions

The focus of this paper is to employ a new topological condition, based on admissibility of the function space topology, to provide existence results for a generalized vector quasi-variational inequality problem and its stronger form as well. The inequality problems involve a set-valued function, and the existence results are proved without using any monotonicity or convexity assumptions on the functions. Further, the solution sets of the inequality problems are shown to be closed and compact.