A note on collectively coincidence theory for lower semicontinuous maps

Abstract

In this paper we present collectively fixed point theory for lower semicontinuous maps. In addition we present coincidence results between $KKM$ type maps and lower semicontinuous maps. Our arguments are based on the Schauder-Tychonoff fixed point theorem and a fixed point result based on $KKM$ self maps on an admissible convex set in a Hausdorff topological vector space. As an application we present a new (Nash) equilibrium result for economies.