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Mat. Zametki, 1969, Volume 6, Issue 1, Pages 47–54 (Mi mz6896)  

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

On the best approximation in the metric of $L$ to certain classes of functions by Haar-system polynomials

N. P. Khoroshko

Dnepropetrovsk State University

Abstract: Let $H_\omega$, $H_\omega^L$ be classes of functions $f(x)$ whose modulus of continuity $\omega(f;t)$ and, respectively, integral modulus of continuity $\omega(f;t)_L$ do not exceed a given modulus of continuity \omega(t)$, while $H_V$ is a class of functions $f(x)$ whose variation $\mathop V\limits_0^1f$ fdoes not exceed a given number $V>0$. Bounds are obtained for the upper limit of the best approximations in the metric of $L$ by Haar-system polynomials on the classes just introduced (on the class $H_\omega^L$ only when $\omega(t)=Kt$). These bounds are exact for class $H_V$ and, in case $\omega(t)$ is convex, also for the classes $H_\omega$ and $H\omega^L$.

Full text: PDF file (403 kB)

English version:
Mathematical Notes, 1969, 6:1, 487–491

Bibliographic databases:

UDC: 517.5
Received: 05.08.1968

Citation: N. P. Khoroshko, “On the best approximation in the metric of $L$ to certain classes of functions by Haar-system polynomials”, Mat. Zametki, 6:1 (1969), 47–54; Math. Notes, 6:1 (1969), 487–491

Citation in format AMSBIB
\Bibitem{Kho69}
\by N.~P.~Khoroshko
\paper On the best approximation in the metric of $L$ to certain classes of functions by Haar-system polynomials
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 1
\pages 47--54
\mathnet{http://mi.mathnet.ru/mz6896}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=249895}
\zmath{https://zbmath.org/?q=an:0188.14002|0179.37201}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 1
\pages 487--491
\crossref{https://doi.org/10.1007/BF01450251}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. B. Vakarchuk, A. N. Shchitov, “Estimates for the error of approximation of classes of differentiable functions by Faber–Schauder partial sums”, Sb. Math., 197:3 (2006), 303–314  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. B. Vakarchuk, A. N. Shchitov, “Estimates for the error of approximation of functions in $L_p^1$ by polynomials and partial sums of series in the Haar and Faber–Schauder systems”, Izv. Math., 79:2 (2015), 257–287  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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