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Matematicheskie Zametki, 2006, Volume 80, Issue 4, Pages 483–489
DOI: https://doi.org/10.4213/mzm2840
(Mi mzm2840)
 

This article is cited in 17 scientific papers (total in 17 papers)

Properties of the metric projection on weakly vial-convex sets and parametrization of set-valued mappings with weakly convex images

M. V. Balashov, G. E. Ivanov

Moscow Institute of Physics and Technology
References:
Abstract: We continue studying the class of weakly convex sets (in the sense of Vial). For points in a sufficiently small neighborhood of a closed weakly convex subset in Hilbert space, we prove that the metric projection on this set exists and is unique. In other words, we show that the closed weakly convex sets have a Chebyshev layer. We prove that the metric projection of a point on a weakly convex set satisfies the Lipschitz condition with respect to a point and the Hölder condition with exponent $1/2$ with respect to a set. We develop a method for constructing a continuous parametrization of a set-valued mapping with weakly convex images. We obtain an explicit estimate for the modulus of continuity of the parametrizing function.
Received: 14.03.2005
English version:
Mathematical Notes, 2006, Volume 80, Issue 4, Pages 461–467
DOI: https://doi.org/10.1007/s11006-006-0163-y
Bibliographic databases:
UDC: 517.982.252
Language: Russian
Citation: M. V. Balashov, G. E. Ivanov, “Properties of the metric projection on weakly vial-convex sets and parametrization of set-valued mappings with weakly convex images”, Mat. Zametki, 80:4 (2006), 483–489; Math. Notes, 80:4 (2006), 461–467
Citation in format AMSBIB
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\issue 4
\pages 483--489
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\jour Math. Notes
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  • https://doi.org/10.4213/mzm2840
  • https://www.mathnet.ru/eng/mzm/v80/i4/p483
  • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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