Fixed Point Theorems on Product Topological Semilattice Spaces, Generalized Abstract Economies and Systems of Generalized Vector Quasi-equilibrium Problems

Abstract

In this paper, we establish fixed point theorems for a family of multivalued maps defined on the product space of topological semilattice spaces. By using our fixed point theorems, we derive a result on the nonempty intersection of sets without convex structure and equilibrium existence theorems for generalized abstract economies with two constraint correspondences. We present some special cases of our results which generalize several known results in the literature. We consider systems of generalized vector quasi-equilibrium problems and their special cases. As an application of our equilibrium existence theorems, we establish some existence results for solutions of systems of generalized vector quasi-equilibrium problems and their special cases. The results of this paper improve and extend several results in the literature.