International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 8, Pages 497-507

Fixed points via a generalized local commutativity

Gerald F. Jungck

Department of Mathematics, Bradley University, Peoria 61625, IL, USA

Received 24 May 2000

Copyright © 2001 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.


Let g:XX. The concept of a semigroup of maps which is “nearly commutative at g” is introduced. We thereby obtain new fixed point theorems for functions with bounded orbit(s) which generalize a recent theorem by Huang and Hong, and results by Jachymski, Jungck, Ohta, and Nikaido, Rhoades and Watson, and others.