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On Constants in the Jackson Stechkin Theorem in the Case of Approximation by Algebraic Polynomials

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Abstract

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.

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Authors and Affiliations

  1. N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    A. G. Babenko

  2. Institute of Natural Sciences and Mathematics, Ural Federal University named after the First President of Russia B. N. Yeltsin, ul. Kuibysheva 48, Yekaterinburg, 620026, Russia

    A. G. Babenko

  3. Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50 384, Wrocław, Poland

    Yu. V. Kryakin

Authors
  1. A. G. Babenko
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  2. Yu. V. Kryakin
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Correspondence to A. G. Babenko or Yu. V. Kryakin.

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Original Russian Text © A.G. Babenko, Yu.V. Kryakin, 2018, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Vol. 303, pp. 26–38.

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Babenko, A.G., Kryakin, Y.V. On Constants in the Jackson Stechkin Theorem in the Case of Approximation by Algebraic Polynomials. Proc. Steklov Inst. Math. 303, 18–30 (2018). https://doi.org/10.1134/S0081543818080035

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