International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 23-28
On a fixed point theorem of Greguš
1Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
2Istituto Matematico, Facolta' Di Architettura, Universita' Di Napoli, Via Monteoliveto 3, Naples 80134, Italy
Received 18 May 1984
Copyright © 1986 Brian Fisher 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.
We consider two selfmaps and of a closed convex subset of a Banach space which are weakly commuting in , i.e.and satisfy the inequalityfor all , in , where . It is proved that if is linear and non-expansive in and such that contains , then and have a unique common fixed point in .