Fixed points via a generalized local commutativity

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.