Fixed Point Theory and Applications
Volume 2005 (2005), Issue 2, Pages 213-217

Asymptotic fixed points for nonlinear contractions

Yong-Zhuo Chen

Department of Mathematics, Computer Science and Engineering, University of Pittsburgh at Bradford, Bradford 16701, PA, USA

Received 29 August 2004; Revised 12 October 2004

Copyright © 2005 Yong-Zhuo Chen. 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.


Recently, W. A. Kirk proved an asymptotic fixed point theorem for nonlinear contractions by using ultrafilter methods. In this paper, we prove his theorem under weaker assumptions. Furthermore, our proof does not use ultrafilter methods.