Abstract

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