In this paper, we establish the existence theorems of simultaneous equilibriums. As consequence of our results, we establish the existence theorem of simultaneous mathematical program and equilibrium problem and existence theorems of generalized vector quasi-saddle point problems .

In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems in finitely continuous topological spaces (in short, FC-spaces). By a maximal element theorem in product FC-spaces, we prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. These theorems improve, unify many important result in recent li...

‎In the paper‎, ‎we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior‎. ‎Then‎, ‎their applications to optimality conditions for quasi-relative efficient solutions are obtained‎. ‎Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...