Open Access

A Note on Asymptotic Contractions

  • Marina Arav1Email author,
  • Francisco Eduardo Castillo Santos2,
  • Simeon Reich3 and
  • Alexander J Zaslavski3
Fixed Point Theory and Applications20062007:039465

DOI: 10.1155/2007/39465

Received: 27 August 2006

Accepted: 16 October 2006

Published: 6 December 2006


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


Authors’ Affiliations

Department of Mathematics and Statistics, Georgia State University
School of Mathematical and Physical Sciences, The University of Newcastle
Department of Mathematics, The Technion–Israel Institute of Technology


  1. Chen Y-Z: Asymptotic fixed points for nonlinear contractions. Fixed Point Theory and Applications 2005,2005(2):213–217. 10.1155/FPTA.2005.213MATHView ArticleGoogle Scholar
  2. Kirk WA: Fixed points of asymptotic contractions. Journal of Mathematical Analysis and Applications 2003,277(2):645–650. 10.1016/S0022-247X(02)00612-1MATHMathSciNetView ArticleGoogle Scholar
  3. Arandelović ID: On a fixed point theorem of Kirk. Journal of Mathematical Analysis and Applications 2005,301(2):384–385. 10.1016/j.jmaa.2004.07.031MathSciNetView ArticleGoogle Scholar
  4. Jachymski J, Jóźwik I: On Kirk's asymptotic contractions. Journal of Mathematical Analysis and Applications 2004,300(1):147–159. 10.1016/j.jmaa.2004.06.037MATHMathSciNetView ArticleGoogle Scholar
  5. Browder FE: On the convergence of successive approximations for nonlinear functional equations. Indagationes Mathematicae 1968, 30: 27–35.MathSciNetView ArticleGoogle Scholar
  6. Rakotch E: A note on contractive mappings. Proceedings of the American Mathematical Society 1962,13(3):459–465. 10.1090/S0002-9939-1962-0148046-1MATHMathSciNetView ArticleGoogle Scholar
  7. Butnariu D, Reich S, Zaslavski AJ: Asymptotic behavior of inexact orbits for a class of operators in complete metric spaces. to appear in Journal of Applied Analysis


© Marina Arav et al. 2007

This article is published under license to BioMed Central Ltd. 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.