Approximate duality for vector quasi-equilibrium problems and applications

In this paper, we introduce new versions of ϵϵ-dual problems of a vector quasi-equilibrium problem with set-valued maps, and we give an ϵϵ-duality result between approximate solutions of the primal and dual problems. As the first application of the main result, we obtain an ϵϵ-duality for a vector quasi-equilibrium problem whose ϵϵ-solutions are understood in the sense of proper efficiency. The second application is devoted to anϵϵ-duality for a vector optimization problem with set-valued maps.