Email this article Approximation Properties of Repeated de la Vallée-Poussin Means for Piecewise Smooth Functions
- Authors: Sharapudinov I.I.1,2, Sharapudinov T.I.1,2, Magomed-Kasumov M.G.1,2
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Affiliations:
- Dagestan Scientific Center
- Southern Mathematical Institute
- Issue: Vol 60, No 3 (2019)
- Pages: 542-558
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172467
- DOI: https://doi.org/10.1134/S0037446619030169
- ID: 172467
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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.
About the authors
I. I. Sharapudinov
Dagestan Scientific Center; Southern Mathematical Institute
Author for correspondence.
Email: sharapudinov@gmail.com
Russian Federation, Makhachkala; Vladikavkaz
T. I. Sharapudinov
Dagestan Scientific Center; Southern Mathematical Institute
Email: rasuldev@gmail.com
Russian Federation, Makhachkala; Vladikavkaz
M. G. Magomed-Kasumov
Dagestan Scientific Center; Southern Mathematical Institute
Author for correspondence.
Email: rasuldev@gmail.com
Russian Federation, Makhachkala; Vladikavkaz
