International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 15-30

Fixed points and continuity for multivalued mappings

Troy Hicks1,2 and B. E. Rhoades1,2

1Department of Mathematics, University of Missouri at Rolla, Rolla 65401, Missouri, USA
2Department of Mathematics, Indiana University, Bloomington 47405, Indiana, USA

Received 31 July 1990; Revised 11 January 1991

Copyright © 1992 Troy Hicks and 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.


Many of the contractive definitions do not require continuity of the map. However, in a previous paper the second author has shown in [1] that, in most cases, the function is continuous at a fixed point. In this paper we show that the same behavior is exhibited for many multivalued mappings.