International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 2, Pages 257-262

Fixed point theorems for compatible multi-valued and single-valued mappings

Hideaki Kaneko1 and Salvatore Sessa2

1Department of Mathematics and Statistics, Old Dominion University, Norfolk 23529, VA, USA
2Universita di Napoli, Facolta di Architettura, Instituto Mathematics, Via Monteoliveto 3, Napoli 80134, Italy

Received 1 July 1987; Revised 1 October 1987

Copyright © 1989 Hideaki Kaneko and Salvatore Sessa. 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.


The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued mapping.