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
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.
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.