Amenability and Fan–Glicksberg theorem for set-valued mappings

Abstract

In this paper, we begin by discussion of some well known results on the existence of left invariant means in the spaces: LUC(S), AP(S) and W AP(S) with Hahn-Banach extension theorem. We then give a new and precise proof of the well known Fan–Glicksberg fixed point theorem. This is then followed by a discussion on some related open problems.