Fixed Point Theory and Applications
Volume 2004 (2004), Issue 1, Pages 31-36

A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle

Jacek Jachymski

Institute of Mathematics, Technical University of Łódź, Żwirki 36, Łódź 90-924, Poland

Received 6 November 2003

Copyright © 2004 Jacek Jachymski. 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.


We show that a discrete fixed point theorem of Eilenberg is equivalent to the restriction of the contraction principle to the class of non-Archimedean bounded metric spaces. We also give a simple extension of Eilenberg's theorem which yields the contraction principle.