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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 3, Pages 695–713
DOI: https://doi.org/10.33048/smzh.2019.60.316 (Mi smj3104) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Approximation properties of repeated de la Vallée-Poussin means for piecewise smooth functions

I. I. Sharapudinovab, T. I. Sharapudinovab, M. G. Magomed-Kasumovab

a Dagestan Scientific Center, Makhachkala, Russia
b Southern Mathematical Institute, Vladikavkaz, Russia
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DOI: https://doi.org/10.33048/smzh.2019.60.316
Abstract: Basing on Fourier’s trigonometric sums and the classical de la Vallée-Poussin means, we introduce the repeated de la Vallée-Poussin means. Under study are the approximation properties of the repeated means for piecewise smooth functions. We prove that the repeated means achieve the rate of approximation for the discontinuous piecewise smooth functions which is one or two order higher than the classical de la Vallée-Poussin means and the partial Fourier sums respectively.
Keywords: repeated de la Vallée-Poussin mean, trigonometric sum, piecewise smooth function.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00486_a
The authors were supported by the Russian Foundation for Basic Research (Grant 16-01-00486).
Received: 10.04.2017
Revised: 10.09.2018
Accepted: 17.10.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 3, Pages 542–558
DOI: https://doi.org/10.1134/S0037446619030169
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: 35R30
Language: Russian
Citation: I. I. Sharapudinov, T. I. Sharapudinov, M. G. Magomed-Kasumov, “Approximation properties of repeated de la Vallée-Poussin means for piecewise smooth functions”, Sibirsk. Mat. Zh., 60:3 (2019), 695–713; Siberian Math. J., 60:3 (2019), 542–558
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Сибирский математический журнал Siberian Mathematical Journal
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