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

This article is cited in 1 scientific paper (total in 1 paper)

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
Received: 30.11.2012
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
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\issue 4
\pages 530--543
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  • 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
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    This publication is cited in the following articles:
    1. R. A. Lasuriya, “Neravenstva tipa Dzheksona v prostranstvakh $S^{(p,q)}(\sigma^{m-1})$”, Matem. zametki, 105:5 (2019), 724–739  mathnet  crossref  elib
  • Математические заметки Mathematical Notes
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