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On Set-Valued Metric Projections

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Linear Operators and Approximation / Lineare Operatoren und Approximation

Abstract

Let E be a normed linear space and G a proximinal linear subspace of E, i.e. such that

$$\matrix{ {{P_G}\left( x \right) = \left\{ {{g_o}G|\left\| {x - {g_o}} \right\| = \mathop {\inf }\limits_{gG} \left\| {x - g} \right\|} \right\} \ne 0} & {\left( {xE} \right).} \cr } $$
(1)

.

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References

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Author information

Authors and Affiliations

  1. Institutul de Matematică Bucureşti, Romania

    Ivan Singer

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  1. Ivan Singer
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Editor information

Editors and Affiliations

  1. Aachen, Germany

    P. L. Butzer

  2. Paris, France

    J.-P. Kahane

  3. Szeged, Hungary

    B. Szökefalvi-Nagy

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© 1972 Birkhäuser Verlag Basel

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Singer, I. (1972). On Set-Valued Metric Projections. In: Butzer, P.L., Kahane, JP., Szökefalvi-Nagy, B. (eds) Linear Operators and Approximation / Lineare Operatoren und Approximation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7283-6_20

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  • DOI: https://doi.org/10.1007/978-3-0348-7283-6_20

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7285-0

  • Online ISBN: 978-3-0348-7283-6

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