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On a Class of Generalized Nonexpansive Mappings

Author

Listed:
  • Simeon Reich

    (Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel)

  • Alexander J. Zaslavski

    (Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel)

Abstract

In our recent work we have introduced and studied a notion of a generalized nonexpansive mapping. In the definition of this notion the norm has been replaced by a general function satisfying certain conditions. For this new class of mappings, we have established the existence of unique fixed points and the convergence of iterates. In the present paper we construct an example of a generalized nonexpansive self-mapping of a bounded, closed and convex set in a Hilbert space, which is not nonexpansive in the classical sense.

Suggested Citation

  • Simeon Reich & Alexander J. Zaslavski, 2020. "On a Class of Generalized Nonexpansive Mappings," Mathematics, MDPI, vol. 8(7), pages 1-8, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1085-:d:379861
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    References listed on IDEAS

    as
    1. Alexander J. Zaslavski, 2016. "Approximate Solutions of Common Fixed-Point Problems," Springer Optimization and Its Applications, Springer, number 978-3-319-33255-0, December.
    2. Alexander J. Zaslavski, 2018. "Algorithms for Solving Common Fixed Point Problems," Springer Optimization and Its Applications, Springer, number 978-3-319-77437-4, December.
    Full references (including those not matched with items on IDEAS)

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