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Contractive Mappings

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

Abstract

In this chapter we consider the class of contractive mappings and show that a typical nonexpansive mapping (in the sense of Baire’s categories) is contractive. We also study nonexpansive mappings which are contractive with respect to a given subset of their domain and establish fixed point and convergence theorems for certain mappings of contractive type which take a closed subset of a complete metric space X into X. We study well-posedness of fixed point problems and construct important examples of nonexpansive mappings. In particular, we construct a contractive self-mapping of a closed interval such that none of its powers is a strict contraction and a nonexpansive mapping with nonuniformly convergent powers.

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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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