A fixed point theorem for non-self set-valued mappings

Abstract

Let X be a complete, metrically convex metric space, K a closed convex subset of X, CB(X) the set of closed and bounded subsets of X. Let F:K→CB(X) satisfying definition (1) below, with the added condition that Fx⫅K for each x∈∂K. Then F has a fixed point in K. This result is an extension to multivalued mappings of a result of Ćirić [1].