International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 32, Pages 2027-2034
Fixed points via a generalized local commutativity: the compact
Department of Mathematics, Bradley University, Peoria, IL 61625, USA
Received 19 July 2001; Revised 6 August 2002
Copyright © 2003 Gerald F. Jungck. 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.
In an earlier paper, the concept of semigroups of self-maps which
are nearly commutative at a function was introduced. We now continue the investigation, but with emphasis
on the compact case. Fixed-point theorems for such semigroups are
obtained in the setting of semimetric and metric spaces.