Fixed Point Theory and Applications 
Volume 2005 (2005), Issue 2, Pages 213-217
doi:10.1155/FPTA.2005.213

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

Abstract

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.