A note on collectively coincidence theory for lower semicontinuous maps

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.