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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 3, Pages 44–52
DOI: https://doi.org/10.4213/faa742 (Mi faa742) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Local Smoothing of Uniformly Smooth Maps

I. G. Tsar'kov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (196 kB) Citations (3)
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DOI: https://doi.org/10.4213/faa742
Abstract: We solve the problem on the uniform approximation of uniformly continuous (smooth) maps by maps having the maximum possible local and uniform smoothness. In particular, we prove that each uniformly continuous map of the Hilbert space l2 into itself can be approximated by locally infinitely differentiable maps having a Lipschitz derivative.
Keywords: approximation, smoothing, local smoothness, uniform smoothness, Lipschitz derivative.
Received: 30.11.2004
English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 3, Pages 200–206
DOI: https://doi.org/10.1007/s10688-006-0031-2
Bibliographic databases:
Document Type: Article
UDC: 517.17
Language: Russian
Citation: I. G. Tsar'kov, “Local Smoothing of Uniformly Smooth Maps”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 44–52; Funct. Anal. Appl., 40:3 (2006), 200–206
Citation in format AMSBIB
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\paper Local Smoothing of Uniformly Smooth Maps
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Linking options:
  • https://www.mathnet.ru/eng/faa742
  • https://doi.org/10.4213/faa742
  • https://www.mathnet.ru/eng/faa/v40/i3/p44
    • This publication is cited in the following 3 articles:
    1. Tsar'kov I.G., “Smoothing of Real-Valued Functions on Uniformly Smooth Spaces”, Russ. J. Math. Phys., 25:3 (2018), 409–414  crossref  mathscinet  zmath  isi  scopus
    2. I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238  mathnet  crossref  crossref  mathscinet  isi  elib
    3. I. G. Tsar'kov, “Local and global continuous ε-selection”, Izv. Math., 80:2 (2016), 442–461  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Full-text PDF :248
    References:86
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