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Mat. Zametki, 2016, Volume 100, Issue 2, Pages 229–247 (Mi mz10588)  

This article is cited in 6 scientific papers (total in 6 papers)

Approximation Properties of de la Vallée-Poussin Means for Piecewise Smooth Functions

M. G. Magomed-Kasumovab

a Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
b Vladikavkaz Scientific Centre of the Russian Academy of Sciences

Abstract: The value of the deviation of a function $f(x)$ from its de la Vallée-Poussin means $V_m^n(f,x)$ with respect to the trigonometric system for classes of piecewise smooth $2\pi$-periodic functions is estimated.

Keywords: de la Vallée-Poussin means, trigonometric system, piecewise smooth function, approximation theory, approximation properties.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00486
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00486.


DOI: https://doi.org/10.4213/mzm10588

Full text: PDF file (530 kB)
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English version:
Mathematical Notes, 2016, 100:2, 229–244

Bibliographic databases:

UDC: 517.521
Received: 14.10.2014
Revised: 15.12.2015

Citation: M. G. Magomed-Kasumov, “Approximation Properties of de la Vallée-Poussin Means for Piecewise Smooth Functions”, Mat. Zametki, 100:2 (2016), 229–247; Math. Notes, 100:2 (2016), 229–244

Citation in format AMSBIB
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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. G. G. Akniev, “Approximation properties of Fourier sums for $2\pi$-periodic piecewise linear continuous functions”, Dagestanskie elektronnye matematicheskie izvestiya, 2016, no. 5, 13–19  mathnet  crossref
    2. G. G. Akniyev, “Discrete least squares approximation of piecewise-linear functions by trigonometric polynomials”, Probl. anal. Issues Anal., 6(24):2 (2017), 3–24  mathnet  crossref  elib
    3. M. G. Magomed-Kasumov, “Otsenka skorosti skhodimosti ryadov po sinusam i kosinusam s koeffitsientami vida $1/k^q$”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 47–51  mathnet  crossref
    4. G. G. Akniev, “Priblizhenie kusochno-lineinykh funktsii diskretnymi summami Fure”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 21–26  mathnet  crossref
    5. G. G. Akniev, “Approksimativnye svoistva diskretnykh summ Fure dlya nekotorykh kusochno-lineinykh funktsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:1 (2018), 4–16  mathnet  crossref  elib
    6. I. I. Sharapudinov, T. I. Sharapudinov, M. G. Magomed-Kasumov, “Approximation properties of repeated de la Vallée-Poussin means for piecewise smooth functions”, Siberian Math. J., 60:3 (2019), 542–558  mathnet  crossref  crossref  isi  elib
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