Fixed Point Theory and Applications 
Volume 2004 (2004), Issue 3, Pages 211-220
doi:10.1155/S1687182004403015

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

Abstract

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.