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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
 Full text:
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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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http://mi.mathnet.ru/eng/mz10175https://doi.org/10.4213/mzm10175 http://mi.mathnet.ru/eng/mz/v98/i4/p530
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This publication is cited in the following articles:
-
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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