FIXED POINT THEOREMS FOR DISCONTINUOUS MAPS ON A NON-CONVEX DOMAIN

Abstract

This paper introduces economists to some ?xed point theorems for discontinuous mappings with non-convex images on a non-convex domain. These theorems have recently been developed based on a new approach by mathematical economists and mathematicians. The new method of proof is ?rst transformed into a sort of metatheorem, which is then used to obtain a set of necessary and suf?cient conditions for a map to have a ?xed point. Some ?xed point theorems for discontinuous maps are then explained in more concrete cases. The formulations are intended for easier applications towards economic models involving discontinuity as well as non-convexity.