International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 289-296

On some weak conditions of commutativity in common fixed point theorems

M. Imdad,1 M. S. Khan,2 and S. Sessa3

1Aligarh Muslim University, Department of Mathematics, Aligarh 202001, India
2King Abdul Aziz University, Faculty of Science, Department of Mathematics, Jeddah 21413, Saudi Arabia
3Universita' di Napoli, Facolta' di Architettura, Istituto Matematico Via Monteoliveto 3, Napoli 80134, Italy

Received 2 September 1986; Revised 4 December 1986

Copyright © 1988 M. Imdad et al. 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.


We generalize common fixed point theorems of Fisher and Sessa in complete metric spaces, using some conditions of weak commutativity between a set-valued mapping and a single-valued mapping. Suitable examples prove that these conditions do not imply each of the others.