Fixed points of multimaps which are not necessarily nonexpansive

Abstract

Let be a nonempty closed bounded convex subset of a Banach space whose characteristic of noncompact convexity is less than and a continuous - -contractive map (which is not necessarily nonexpansive) from to satisfying an inwardness condition, where is the family of all nonempty compact convex subsets of . It is proved that has a fixed point. Some fixed points results for noncontinuous maps are also derived as applications. Our result contains, as a special case, a recent result of Benavides and Ramírez (2004).