Fixed Points for Contractive Multifunctions

Let F:X → X be a point closed multifunction on the bounded metric space $(X,d)$. Let d denote the Hausdorff metric for the nonempty closed subsets of X. Then F is contractive iff d(F(x),F(y)) < d(x,y) for all x,y ∈ X. We give conditions under which contractive multifunctions have fixed points.