International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 8, Pages 497-507
doi:10.1155/S0161171201005312
Fixed points via a generalized local commutativity
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.
Abstract
Let g:X→X. 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.