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Nearby sets and centers

Approximation Theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 1354)

Abstract

Let us consider a Banach space X and a class C of subsets in X. Let c be a (Chebyshev) center of CεC; it is known that under some assumptions on Cand/or X, if {Cn} is a sequence from C converging to C according to the Hausdorff metric h(Cn,C), then c is the limit of a sequence of centers of Cn. Here we shall discuss some estimates of the distance between cn and c, in terms of h(Cn,C).

Keywords

  • Hilbert Space
  • Banach Space
  • Nonexpansive Mapping
  • Convex Space
  • Finite Dimensional Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1988 Springer-Verlag

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Baronti, M., Papini, P.L. (1988). Nearby sets and centers. In: Gómez-Fernandez, J.A., Guerra-Vázquez, F., López-Lagomasino, G., Jiménez-Pozo, M.A. (eds) Approximation and Optimization. Lecture Notes in Mathematics, vol 1354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089585

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  • DOI: https://doi.org/10.1007/BFb0089585

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50443-6

  • Online ISBN: 978-3-540-46005-3

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