Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 39465, 6 pages
doi:10.1155/2007/39465
A note on asymptotic contractions
Marina Arav1
, Francisco Eduardo Castillo Santos2
, Simeon Reich3
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
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.