Fixed Point Theory and Applications
Volume 2004 (2004), Issue 3, Pages 211-220

Generic convergence of iterates for a class of nonlinear mappings

Simeon Reich1,2 and Alexander J. Zaslavski1

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 K 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 K converge uniformly on K to the unique fixed point of this typical element.