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Generic convergence of iterates for a class of nonlinear mappings

Fixed Point Theory and Applications volume 2004, Article number: 480953 (2004) Cite this article

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.

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Authors and Affiliations

  1. Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, 32000, Israel

    Simeon Reich & Alexander J Zaslavski

  2. Department of Mathematics, University of California, Santa Barbara, CA, 93106-3080, USA

    Simeon Reich

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  1. Simeon Reich
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  2. Alexander J Zaslavski
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Correspondence to Simeon Reich.

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Reich, S., Zaslavski, A.J. Generic convergence of iterates for a class of nonlinear mappings. Fixed Point Theory Appl 2004, 480953 (2004). https://doi.org/10.1155/S1687182004403015

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  • DOI: https://doi.org/10.1155/S1687182004403015