Fixed Point Theory and Applications 
Volume 2004 (2004), Issue 1, Pages 31-36
doi:10.1155/S1687182004311010

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

Abstract

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.