R. A. Lasuriya, “Direct and Inverse Theorems on the Approximation of Functions by Fourier–Laplace Sums in the Spaces $S^{(p,q)}(\sigma^{m-1})$”, Mat. Zametki, 98:4 (2015), 530–543; Math. Notes, 98:4 (2015), 601

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Matematicheskie Zametki, 2015, Volume 98, Issue 4, Pages 530–543
DOI: https://doi.org/10.4213/mzm10175 (Mi mzm10175)

This article is cited in 4 scientific papers (total in 4 papers)

Direct and Inverse Theorems on the Approximation of Functions by Fourier–Laplace Sums in the Spaces

$S^{(p,q)}(\sigma^{m-1})$

R. A. Lasuriya

Abkhazian State University

Full-text PDF (540 kB) Citations (4)

References:

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DOI: https://doi.org/10.4213/mzm10175

Abstract: In this paper, we prove direct and inverse theorems on the approximation of functions by Fourier–Laplace sums in the spaces

$S^{(p,q)}(\sigma^{m-1})$ ,

$m\ge 3$ , in terms of best approximations and moduli of continuity and consider the constructive characteristics of function classes defined by the moduli of continuity of their elements. The given statements generalize the results of the author's work carried out in 2007.

Keywords: approximation of functions, Fourier–Laplace sum, the spaces

$S^{(p,q)}(\sigma^{m-1})$ , modulus of continuity, Parseval's equality, Jackson-type inequality, Gegenbauer polynomial, Bernstein–Stechkin–Timan-type inequality.

Received: 30.11.2012
Revised: 05.03.2015

English version:
Mathematical Notes, 2015, Volume 98, Issue 4, Pages 601–612
DOI: https://doi.org/10.1134/S0001434615090278

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: R. A. Lasuriya, “Direct and Inverse Theorems on the Approximation of Functions by Fourier–Laplace Sums in the Spaces

$S^{(p,q)}(\sigma^{m-1})$ ”, Mat. Zametki, 98:4 (2015), 530–543; Math. Notes, 98:4 (2015), 601–612

Citation in format AMSBIB

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\issue 4

\pages 530--543

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\jour Math. Notes

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Linking options:

https://www.mathnet.ru/eng/mzm10175

https://doi.org/10.4213/mzm10175

https://www.mathnet.ru/eng/mzm/v98/i4/p530

This publication is cited in the following 4 articles:

R. A. Lasuriya, “On Quantities of the Type of Modulus of Continuity and Analogs of $K$ -Functionals in the Spaces $S^{(p,q)}(\sigma^{m-1})$ ”, Math. Notes, 113:2 (2023), 255–266
El Ouadih S., Daher R., Tyr O., Saadi F., “Equivalence of K-Functionals and Moduli of Smoothness Generated By the Beltrami-Laplace Operator on the Spaces S-(P,S-Q)(SIGMA(M-1))”, Rend. Circ. Mat. Palermo, 71:1 (2022), 445–458
R. A. Lasuriya, “Inverse Approximation Theorems in the Spaces $S^{(p,q)}(\sigma^{m-1})$ ”, Math. Notes, 110:1 (2021), 80–91
R. A. Lasuriya, “Jackson-Type Inequalities in the Spaces $S^{(p,q)}(\sigma^{m-1})$ ”, Math. Notes, 105:5 (2019), 707–719

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

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Abstract page:	387
Full-text PDF :	170
References:	64
First page:	17

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