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
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.