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.

Automated summary

This paper utilizes a new topological condition based on admissibility of the function space topology to establish existence results for a generalized vector quasi-variational inequality problem and its stronger form. The existence results are proved without relying on monotonicity or convexity assumptions on the functions. Additionally, the solution sets of the inequality problems are demonstrated to be closed and compact.