Fixed Point and Maximal Element Theorems with Application to Abstract Economy

Abstract

The main object of this paper is to establish some fixed point theorems for a family of multivalued maps defined on the product of Hausdorff topological vector spaces. From our fixed point theorems, we derive some maximal element theorems for a family of multivalued maps. As an application of our results, we prove an equilibrium existence theorem for non-compact abstract economy. The results of this paper generalize known results in the literature.