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

Rhoades, B. E.

doi:10.1155/S0161171297000021

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International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 9-12
http://dx.doi.org/10.1155/S0161171297000021

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

B. E. Rhoades

Department of Mathematics, Indiana University, Bloomington 47405, Indiana, USA

Received 29 September 1994

Copyright © 1997 Hindawi Publishing Corporation. 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].