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Matematicheskie Zametki, 1970, Volume 8, Issue 5, Pages 583–594 (Mi mzm7006)  
This article is cited in 6 scientific papers (total in 6 papers)

The existence of a best approximating element in (F)(F)-space with integral metric

A. L. Garkavi

V. V. Kuibyshev Military Engineering Academy
Full-text PDF (869 kB) Citations (6)
Abstract: The existence is proved of a best approximation element in finite-dimensional subspaces of linear metric spaces of a class containing, in particular, the space S[0,1]S[0,1] of measurable functions.
Received: 12.02.1970
English version:
Mathematical Notes, 1970, Volume 8, Issue 5, Pages 797–802
DOI: https://doi.org/10.1007/BF01146935
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: A. L. Garkavi, “The existence of a best approximating element in (F)(F)-space with integral metric”, Mat. Zametki, 8:5 (1970), 583–594; Math. Notes, 8:5 (1970), 797–802
Citation in format AMSBIB
\Bibitem{Gar70}
\by A.~L.~Garkavi
\paper The existence of a~best approximating element in $(F)$-space with integral metric
\jour Mat. Zametki
\yr 1970
\vol 8
\issue 5
\pages 583--594
\mathnet{http://mi.mathnet.ru/mzm7006}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=276713}
\zmath{https://zbmath.org/?q=an:0234.46017}
\transl
\jour Math. Notes
\yr 1970
\vol 8
\issue 5
\pages 797--802
\crossref{https://doi.org/10.1007/BF01146935}
Linking options:
  • https://www.mathnet.ru/eng/mzm7006
  • https://www.mathnet.ru/eng/mzm/v8/i5/p583
    • This publication is cited in the following 6 articles:
    1. B. V. Simonov, “Asymmetric approximations of functions of several variables in function spaces”, Russian Math. (Iz. VUZ), 49:8 (2005), 46–52  mathnet  mathscinet
    2. A. A. Vasil'eva, “Closed spans in vector-valued function spaces and their approximative properties”, Izv. Math., 68:4 (2004), 709–747  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. B. V. Simonov, “On the Element of Best Nonsymmetric Approximation in Spaces with Nonsymmetric Quasinorm”, Math. Notes, 74:6 (2003), 853–863  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. L. Garkavi, “On minimization of integral functionals on the space of measurable functions”, Math. Notes, 54:5 (1993), 1093–1099  mathnet  crossref  mathscinet  zmath  isi  elib
    5. N. K. Rakhmetov, “On finite-dimension Chebyshev subspaces of spaces with an integral metric”, Math. USSR-Sb., 74:2 (1993), 361–380  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. È. A. Storozhenko, V. G. Krotov, P. Oswald, “Direct and converse theorems of Jackson type in $L^p$ spaces, $0<p<1$”, Math. USSR-Sb., 27:3 (1975), 355–374  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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