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 Mat. Zametki, 2015, Volume 98, Issue 4, Pages 530–543 (Mi mz10175)

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

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.

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

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English version:
Mathematical Notes, 2015, 98:4, 601–612

Bibliographic databases:

UDC: 517.5
Revised: 05.03.2015

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
\Bibitem{Las15} \by R.~A.~Lasuriya \paper Direct and Inverse Theorems on the Approximation of Functions by Fourier--Laplace Sums in the Spaces $S^{(p,q)}(\sigma^{m-1})$ \jour Mat. Zametki \yr 2015 \vol 98 \issue 4 \pages 530--543 \mathnet{http://mi.mathnet.ru/mz10175} \crossref{https://doi.org/10.4213/mzm10175} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438510} \elib{https://elibrary.ru/item.asp?id=24850159} \transl \jour Math. Notes \yr 2015 \vol 98 \issue 4 \pages 601--612 \crossref{https://doi.org/10.1134/S0001434615090278} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000363520200027} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84945136289} 

• http://mi.mathnet.ru/eng/mz10175
• https://doi.org/10.4213/mzm10175
• http://mi.mathnet.ru/eng/mz/v98/i4/p530

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

This publication is cited in the following articles:
1. R. A. Lasuriya, “Jackson-Type Inequalities in the Spaces $S^{(p,q)}(\sigma^{m-1})$”, Math. Notes, 105:5 (2019), 707–719
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