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

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

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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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
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
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