International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 9-12
doi:10.1155/S0161171297000021
A fixed point theorem for non-self set-valued mappings
Department of Mathematics, Indiana University, Bloomington 47405, Indiana, USA
Received 29 September 1994
Copyright © 1997 B. E. Rhoades. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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].