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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 303, Pages 17–25
DOI: https://doi.org/10.1134/S0371968518040027 (Mi tm3939) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Selections of the best and near-best approximation operators and solarity

A. R. Alimovab

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (184 kB) Citations (3)
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DOI: https://doi.org/10.1134/S0371968518040027
Abstract: In a finite-dimensional Banach space, a closed set with lower semicontinuous metric projection is shown to have a continuous selection of the near-best approximation operator. Such a set is known to be a sun. In the converse question of the stability of best approximation by suns, it is proved that a strict sun in a finite-dimensional Banach space of dimension at most 3 is a P-sun, has a contractible set of nearest points, and admits a continuous ε-selection from the operator of near-best approximation for any ε>0. A number of approximative and geometric properties of sets with lower semicontinuous metric projection are obtained.
Keywords: lower semicontinuity of the metric projection, selection of the metric projection, sun, strict sun, near-best approximation.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00333_а
19-01-00332_а
Ministry of Education and Science of the Russian Federation НШ-6222.2018.1
The work was supported by the Russian Foundation for Basic Research (project nos. 18-01-00333 and 19-01-00332-a) and by a grant of the President of the Russian Federation (project no. NSh-6222.2018.1).
Received: October 1, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 303, Pages 10–17
DOI: https://doi.org/10.1134/S0081543818080023
Bibliographic databases:
Document Type: Article
UDC: 517.982.256+517.982.252
Language: Russian
Citation: A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 17–25; Proc. Steklov Inst. Math., 303 (2018), 10–17
Citation in format AMSBIB
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\paper Selections of the best and near-best approximation operators and solarity
\inbook Harmonic analysis, approximation theory, and number theory
\bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 303
\pages 17--25
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3939}
\crossref{https://doi.org/10.1134/S0371968518040027}
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  • https://www.mathnet.ru/eng/tm/v303/p17
    • This publication is cited in the following 3 articles:
    1. A. R. Alimov, “Monotone path-connectedness of strict suns”, Lobachevskii J. Math., 43:3 (2022), 519  crossref  mathscinet
    2. A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space ℓn∞”, Math. Notes, 108:3 (2020), 309–317  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. R. Alimov, “Solarity of sets in max-approximation problems”, J. Fixed Point Theory Appl., 21:3 (2019), UNSP 76  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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