- Research Article
- Open access
- Published:
Common fixed point theorems for compatible self-maps of Hausdorff topological spaces
Fixed Point Theory and Applications volume 2005, Article number: 645183 (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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Jungck, G.F. Common fixed point theorems for compatible self-maps of Hausdorff topological spaces. Fixed Point Theory Appl 2005, 645183 (2005). https://doi.org/10.1155/FPTA.2005.355
Received:
Revised:
Published:
DOI: https://doi.org/10.1155/FPTA.2005.355