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Mat. Zametki, 1972, Volume 11, Issue 5, Pages 491–498 (Mi mz9815)  

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

Best approximations by rational functions with respect to the Hausdorff distance

K. N. Lungu

Moscow Institute of Railway Transport Engineers

Abstract: Inverse theorems on the best approximations of plane sets in a Hausdorff metric by means of rational functions are cited. It is shown, among other things, that if $R_{n,r}(F,[a,b])=o(1/n)$, then there exists a set $P\subset[a,b]$ of complete measure over which $F$ constitutes a single-valued function.

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English version:
Mathematical Notes, 1972, 11:5, 300–304

Bibliographic databases:

UDC: 517.5
Received: 02.06.1971

Citation: K. N. Lungu, “Best approximations by rational functions with respect to the Hausdorff distance”, Mat. Zametki, 11:5 (1972), 491–498; Math. Notes, 11:5 (1972), 300–304

Citation in format AMSBIB
\Bibitem{Lun72}
\by K.~N.~Lungu
\paper Best approximations by rational functions with respect to the Hausdorff distance
\jour Mat. Zametki
\yr 1972
\vol 11
\issue 5
\pages 491--498
\mathnet{http://mi.mathnet.ru/mz9815}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=303185}
\zmath{https://zbmath.org/?q=an:0247.41010}
\transl
\jour Math. Notes
\yr 1972
\vol 11
\issue 5
\pages 300--304
\crossref{https://doi.org/10.1007/BF01158641}


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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. E. P. Dolzhenko, E. A. Sevast'yanov, “Approximations of functions in the Hausdorff metric by piecewise monotonic (in particular, rational) functions”, Math. USSR-Sb., 30:4 (1976), 449–477  mathnet  crossref  mathscinet  zmath  isi
    2. A. P. Petukhov, “On the dependence of properties of the graph of a function on the degree of various approximations”, Math. USSR-Izv., 38:1 (1992), 155–177  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математические заметки Mathematical Notes
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