Fixed Point Theory and Applications 
Volume 2007 (2007), Article ID 39465, 6 pages
doi:10.1155/2007/39465
Research Article

A Note on Asymptotic Contractions

Marina Arav,1 Francisco Eduardo Castillo Santos,2 Simeon Reich,3 and Alexander J. Zaslavski3

 1Department of Mathematics and Statistics, Georgia State University, Atlanta 30303, GA, USA
2School of Mathematical and Physical Sciences, The University of Newcastle, Newcastle 2308, NSW, Australia
3Department of Mathematics, The Technion–Israel Institute of Technology, Haifa 32000, Israel
Received 27 August 2006; Revised 16 October 2006; Accepted 16 October 2006

Recommended by Brailey Sims

Abstract

We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.