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Handbook of Metric Fixed Point Theory pp 201–238Cite as

Stability of the Fixed Point Property for Nonexpansive Mappings

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Abstract

In 1971 Zidler [Zi 71] showed that every separable Banach space (X, ‖·‖) admits an equivalent renorming, (X, ‖·‖0), which is uniformly convex in every direction (UCED), and consequently it has weak normal structure and so the weak fixed point property (WFPP) [D-J-S 71].

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Author information

Authors and Affiliations

  1. Department d’Anàlisi Matematica Facultat de Matematiques, Universitat de Valencia, Doctor Moliner 50, 46100, Burfassot, Spain

    Jesús Garcia-Falset & Enrique Llorens-Fuster

  2. Department de Matematiques, Universitat de Malaga, campus de Teatinos, 29071, Malaga, Spain

    Antonio Jiménez-Melado

Authors
  1. Jesús Garcia-Falset
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  2. Antonio Jiménez-Melado
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  3. Enrique Llorens-Fuster
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The University of Iowa, Iowa City, IA, USA

    William A. Kirk

  2. School of Mathematical and Physical Sciences, The University of Newcastle, Newcastle, Australia

    Brailey Sims

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Garcia-Falset, J., Jiménez-Melado, A., Llorens-Fuster, E. (2001). Stability of the Fixed Point Property for Nonexpansive Mappings. In: Kirk, W.A., Sims, B. (eds) Handbook of Metric Fixed Point Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1748-9_7

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  • DOI: https://doi.org/10.1007/978-94-017-1748-9_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5733-4

  • Online ISBN: 978-94-017-1748-9

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