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Minimal and Closest Points Nonexpansive and Quasi-Nonexpansive Retractions in Real Banach Spaces

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Convexity and Its Applications

Summary

The notions indicated in the title and related ones have been studied independently by various authors. Some characterizations of inner product spaces have been given in terms of properties of minimal and closest points, or by considering special retractions. Yet, the very strong connections existing among the above notions have not been considered in full. This present analysis shows that some results can be obtained from older ones, and other results can be restated in a sharper form using known facts and simple connections relating the various notions.

Work performed under the auspices of the G.N.A.F.A. of the C.N.R. (National Council of Research of Italy).

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Authors and Affiliations

  1. Istituto Matematico “Salvatore Pincherle”, Università di Bologna, Piazza di Porta San Donato 5, I-40127, Bologna, Italy

    Pier Luigi Papini

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  1. Pier Luigi Papini
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  1. Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Gusshausstrasse 25-27, A-1040, Wien, Austria

    Peter M. Gruber

  2. Lehrstuhl für Mathematik II, Universität Siegen, Hölderlinstrasse 3, D-5900, Siegen 21, Germany

    Jörg M. Wills

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Papini, P.L. (1983). Minimal and Closest Points Nonexpansive and Quasi-Nonexpansive Retractions in Real Banach Spaces. In: Gruber, P.M., Wills, J.M. (eds) Convexity and Its Applications. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5858-8_10

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  • DOI: https://doi.org/10.1007/978-3-0348-5858-8_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5860-1

  • Online ISBN: 978-3-0348-5858-8

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