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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 4, Pages 246–253 (Mi timm658)  

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

On the Jackson–Stechkin inequality for algebraic polynomials

A. V. Mironenko

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The Jackson–Stechkin inequality is considered, which estimates the value of the best uniform approximation of a continuous function by algebraic polynomials on a closed interval in terms of values of the modulus of continuity of the approximated function. A variant of the inequality with second-order modulus of continuity and explicit specification of the argument of the modulus of continuity and the constant is proved.

Keywords: Jackson inequality, approximation by algebraic polynomials, modulus of continuity.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 273, suppl. 1, S116–S123

Bibliographic databases:

UDC: 517.518.82
Received: 01.05.2010

Citation: A. V. Mironenko, “On the Jackson–Stechkin inequality for algebraic polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 246–253; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S116–S123

Citation in format AMSBIB
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\by A.~V.~Mironenko
\paper On the Jackson--Stechkin inequality for algebraic polynomials
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 4
\pages 246--253
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 273
\issue , suppl. 1
\pages S116--S123
\crossref{https://doi.org/10.1134/S0081543811050129}
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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. Gocheva-Ilieva S.G., Feschiev I.H., “New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series”, Abstract Appl. Anal., 2013, 523618  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. G. Babenko, Yu. V. Kryakin, “On constants in the Jackson–Stechkin theorem in the case of approximation by algebraic polynomials”, Proc. Steklov Inst. Math., 303 (2018), 18–30  mathnet  crossref  crossref  isi  elib
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