Fixed Point Theory and Applications
Volume 2004 (2004), Issue 3, Pages 211-220
Generic convergence of iterates for a class of nonlinear mappings
1Department of Mathematics, The Technion – Israel Institute of Technology, Haifa 32000, Israel
2Department of Mathematics, University of California, Santa Barbara 93106-3080, CA, USA
Received 4 March 2004
Copyright © 2004 Simeon Reich and Alexander J. Zaslavski. 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.
Let be a nonempty, bounded, closed, and convex subset of a
Banach space. We show that the iterates of a typical element
(in the sense of Baire's categories) of a class of continuous
self-mappings of converge uniformly on to the unique
fixed point of this typical element.