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Mat. Zametki, 2014, Volume 96, Issue 4, Pages 588–595 (Mi mz10228)  

This article is cited in 2 scientific papers (total in 2 papers)

The Linearity Coefficient of Metric Projections onto One-Dimensional Chebyshev Subspaces of the Space $C$

K. V. Chesnokova

M. V. Lomonosov Moscow State University

Abstract: The paper deals with the operator of metric projection onto an arbitrary one-dimensional Chebyshev subspace $\langle\varphi\rangle$ of the space $C[K]$ of real-valued functions defined and continuous on a Hausdorff compact set $K$. The linearity coefficient of the operator is calculated in terms of the parameters of the generating function $\varphi$. As a consequence, a new estimate of the Lipschitz constant of the operator is obtained.

Keywords: metric projection operator, Chebyshev subspace, Hausdorff compact set $K$, Lipschitz constant of an operator, Lipschitz condition, Banach space.

DOI: https://doi.org/10.4213/mzm10228

Full text: PDF file (406 kB)
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English version:
Mathematical Notes, 2014, 96:4, 556–562

Bibliographic databases:

UDC: 517.982.256
Received: 20.11.2012
Revised: 19.11.2013

Citation: K. V. Chesnokova, “The Linearity Coefficient of Metric Projections onto One-Dimensional Chebyshev Subspaces of the Space $C$”, Mat. Zametki, 96:4 (2014), 588–595; Math. Notes, 96:4 (2014), 556–562

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730  mathnet  crossref  mathscinet
    2. A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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