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Genericity in Nonlinear Analysis pp 119–179Cite as

Contractive Mappings

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Part of the book series: Developments in Mathematics ((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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Authors and Affiliations

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

    Simeon Reich & Alexander J. Zaslavski

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  1. Simeon Reich
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  2. Alexander J. Zaslavski
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Reich, S., Zaslavski, A.J. (2014). Contractive Mappings. In: Genericity in Nonlinear Analysis. Developments in Mathematics, vol 34. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9533-8_3

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