Open Access

Common fixed point theorems for compatible self-maps of Hausdorff topological spaces

Fixed Point Theory and Applications20052005:645183

https://doi.org/10.1155/FPTA.2005.355

Received: 13 July 2004

Published: 25 October 2005

Abstract

The concept of proper orbits of a map is introduced and results of the following type are obtained. If a continuous self-map of a Hausdorff topological space has relatively compact proper orbits, then has a fixed point. In fact, has a common fixed point with every continuous self-map of which is nontrivially compatible with . A collection of metric and semimetric space fixed point theorems follows as a consequence. Specifically, a theorem by Kirk regarding diminishing orbital diameters is generalized, and a fixed point theorem for maps with no recurrent points is proved.

Authors’ Affiliations

(1)
Department of Mathematics, Bradley University

Copyright

© Jungck 2005