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Fixed Point Results and Convergence of Powers of Operators

  • Simeon Reich
  • Alexander J. Zaslavski
Part of the Developments in Mathematics book series (DEVM, volume 34)

Abstract

In this chapter we establish existence and uniqueness of a fixed point for a generic mapping, convergence of iterates of a generic nonexpansive mapping, stability of the fixed point under small perturbations of a mapping and many other results. In particular, for a given nonempty, bounded, closed and convex subset K 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.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Simeon Reich
    • 1
  • Alexander J. Zaslavski
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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