MAXIMAL ELEMENT THEOREM WITH APPLICATIONS TO GENERALIZED ABSTRACT ECONOMIES AND SYSTEM OF QUASI-EQUILIBRIUM PROBLEMS ON HADAMARD MANIFOLDS

In this paper, we establish a maximal element theorem for a finite family of multivalued maps in the setting of Hadamard manifolds. As an application of our maximal element theorem, we prove the existence of solutions of generalized abstract economies with two constraint correspondences. We also consider the system of quasi-equilibrium problems and system of generalized implicit quasi-equilibrium problems. We first derive the existence result for a solution of system of quasi-equilibrium problems and then by using this result, we prove the existence of a solution of system of a generalized implicit quasi-equilibrium problems. An as application of system of quasi-equilibrium problems, we prove the existence result of constrained Nash equilibrium problem for real-valued functions with finite number of players.