Approximate duality for vector quasi-equilibrium problems and applications

In this paper, we introduce new versions of epsilon-dual problems of a vector quasi-equilibrium problem with set-valued maps, and we give an epsilon-duality result between approximate solutions of the primal and dual problems. As the first application of the main result, we obtain an epsilon-duality for a vector quasi-equilibrium problem whose epsilon-solutions are understood in the sense of proper efficiency. The second application is devoted to an epsilon-duality for a vector optimization problem with set-valued maps. (C) 2010 Elsevier Ltd. All rights reserved.