Generalization of browder's fixed point theorem and its applications

Abstract

From an infinite dimensional version of a generalization, dueto Peleg, of the Knaster-Kuratowski-Mazurkiewicz's theorem, we obtain a generalization of Browder's fixed point theorem, for multi-valued mappings from the product of a finite family of non-empty compact convex sets ( each in a Hausdorff topological vector space) into each of its factors. By applying this thorem, we deduce sorne Ky Fan type inequalities, from one of which a generalization of the Ky Fan's intersection theorem on sets with convex sections is obtained.