R. M. Trigub, “The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials”, Sb. Math., 204:12 (2013), 1819

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Sbornik: Mathematics, 2013, Volume 204, Issue 12, Pages 1819–1838
DOI: https://doi.org/10.1070/SM2013v204n12ABEH004362 (Mi sm8228)

This article is cited in 9 scientific papers (total in 9 papers)

The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials

R. M. Trigub

Donetsk National University

English version PDF (486 kB) Citations (9) Russian version article

References:

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DOI: https://doi.org/10.1070/SM2013v204n12ABEH004362

Abstract: The paper concerns the approximation properties of the Bernstein-Stechkin summability method for trigonometric Fourier series. The Jackson-Stechkin theorem is refined. Moreover, for any continuous periodic function not only is the exact upper estimate for approximation found, a lower estimate of the same order is also put forward. To do this special moduli of smoothness and the

K

$K$ -functional are introduced.
Bibliography: 16 titles.

Keywords:

B

$B$ -spline, modulus of smoothness,

K

$K$ -functional, Fourier transform of a measure, Fourier multiplier.

Received: 28.02.2013 and 10.05.2013

Bibliographic databases:

Document Type: Article

UDC: 517.51

MSC: 42A10

Language: English

Original paper language: Russian

Citation: R. M. Trigub, “The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials”, Sb. Math., 204:12 (2013), 1819–1838

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm8228

https://doi.org/10.1070/SM2013v204n12ABEH004362

https://www.mathnet.ru/eng/sm/v204/i12/p127

This publication is cited in the following 9 articles:

Yurii Kolomoitsev, Tetiana Lomako, “Sharp Lp-error estimates for sampling operators”, Journal of Approximation Theory, 294 (2023), 105941
Roald Trigub, “Relation between Fourier series and Wiener algebras”, UMB, 18:1 (2021), 80
Trigub R.M., “On Various Moduli of Smoothness and K-Functionals”, Ukr. Math. J., 72:7 (2020), 1131–1163
R. M. Trigub, “O raznykh modulyakh gladkosti i K -funktsionalakh”, Ukr. Mat. Zhurn., 72:7 (2020), 971
Trigub R.M., “On the Approximation of Functions By Polynomials and Entire Functions of Exponential Type”, Ukr. Math. J., 71:2 (2019), 333–341
Yu. Kolomoitsev, “On moduli of smoothness and averaged differences of fractional order”, Fract. Calc. Appl. Anal., 20:4 (2017), 988–1009
S. Yu. Artamonov, “Quality of Approximation by Fourier Means in Terms of General Moduli of Smoothness”, Math. Notes, 98:1 (2015), 3–10
A. Penskoi, “Generalized Lawson Tori and Klein Bottles”, J. Geom. Anal., 25:4 (2015), 2645–2666
Ol'ga V. Kotova, Roald M. Trigub, “Approximative properties of the summation methods of Fourier integrals”, J Math Sci, 211:5 (2015), 668

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	559
Russian version PDF:	203
English version PDF:	27
References:	85
First page:	57

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