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Generic convergence of iterates for a class of nonlinear mappings

Fixed Point Theory and Applications20042004:480953

https://doi.org/10.1155/S1687182004403015

Received: 4 March 2004

Published: 26 August 2004

Abstract

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.

Authors’ Affiliations

(1)
Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, Israel
(2)
Department of Mathematics, University of California, Santa Barbara, USA

Copyright

© Reich and Zaslavski 2004

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