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Mathematical Notes

, Volume 104, Issue 5–6, pp 678–682 | Cite as

On Selections from the Best n-Nets

  • Yu. Yu. DruzhininEmail author
Article
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Abstract

The discontinuity of any selection from a best n-net for n ≥ 2 in an arbitrary not strictly convex Banach space is proved. It is also proved that there is no Lipschitz selection on an arbitrary Banach space of dimension at least 2 whose unit sphere contains an attainable point of smoothness.

Keywords

Banach space selection best n-net Chebyshev center 

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References

  1. 1.
    A. L. Garkavi, “The theory of best approximation in normed linear spaces,” in Itogi Nauki. Ser.Matematika. Mat. Anal., 1967 (VINITI, Moscow, 1969), Vol. 1967, pp. 75–132 [Progr.Math. 8, 83–150 (1970)].Google Scholar
  2. 2.
    Yu. Yu. Druzhinin, “Existence of a Lipschitz selection of the Chebyshev-centermap,” Mat. Sb. 204 (5), 25–44 (2013) [Sb.Math. 204 (5), 641–660 (2013)].MathSciNetCrossRefGoogle Scholar
  3. 3.
    T. Bonnesen and W. Fenchel, Theory of Convex Bodies, Ed. by L. Boron, C. Christenson, and B. Smith (BCS Associates,Moscow, ID, 1987; Fazis, Moscow, 2002).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.State-Funded Educational Institution Lycée 1158MoscowRussia

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