On Constants in the Jackson Stechkin Theorem in the Case of Approximation by Algebraic Polynomials
- Autores: Babenko A.G.1,2, Kryakin Y.V.3
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Afiliações:
- N. N. Krasovskii Institute of Mathematics and Mechanics
- Institute of Natural Sciences and Mathematics
- Institute of Mathematics
- Edição: Volume 303, Nº 1 (2018)
- Páginas: 18-30
- Seção: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/175657
- DOI: https://doi.org/10.1134/S0081543818080035
- ID: 175657
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Resumo
New estimates are proved for the constants J(k, α) in the classical Jackson–Stechkin inequality En−1(f) ≤ J(k, α)ωk(f,απ/n), α > 0, in the case of approximation of functions f ∈ C[−1, 1] by algebraic polynomials. The main result of the paper implies the following two-sided estimates for the constants: 1/2 ≤ J(2k, α) < 10, n ≥ 2k(2k − 1), α ≥ 2.
Sobre autores
A. Babenko
N. N. Krasovskii Institute of Mathematics and Mechanics; Institute of Natural Sciences and Mathematics
Autor responsável pela correspondência
Email: babenko@imm.uran.ru
Rússia, ul. S. Kovalevskoi 16, Yekaterinburg, 620990; ul. Kuibysheva 48, Yekaterinburg, 620026
Yu. Kryakin
Institute of Mathematics
Autor responsável pela correspondência
Email: kryakin@math.uni.wroc.pl
Polônia, pl. Grunwaldzki 2/4, Wrocław, 50 384
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