Fejer means of rational Fourier – Chebyshev series and approximation of function |x|s

Authors

Keywords:

Fourier – Chebyshev series, partial sums, Fejer means, modulus of continuity, uniform convergence, asymptotic estimates, exact constants

Abstract

Approximation properties of Fejer means of Fourier series by Chebyshev – Markov system of algebraic fractions and approximation by Fejer means of function |x|s, 0 < s < 2, on the interval [−1,1], are studied. One orthogonal system of Chebyshev – Markov algebraic fractions is considers, and Fejer means of the corresponding rational Fourier – Chebyshev series is introduce. The order of approximations of the sequence of Fejer means of continuous functions on a segment in terms of the continuity module and sufficient conditions on the parameter providing uniform convergence are established. A estimates of the pointwise and uniform approximation of the function |x|s, 0 < s < 2, on the interval [−1,1], the asymptotic expressions under n→∞ of majorant of uniform approximations, and the optimal value of the parameter, which provides the highest rate of approximation of the studied functions are sums of rational use of Fourier – Chebyshev are found. 

Author Biographies

  • Pavel G. Patseika, Yanka Kupala State University of Grodno, 22 Ažeška Street, Hrodna 230023, Belarus

    postgraduate student at the department of fundamental and applied mathematics, faculty of mathematics and informatics

  • Yauheni A. Rouba , Yanka Kupala State University of Grodno, 22 Ažeška Street, Hrodna 230023, Belarus

    doctor of science (physics and mathematics), full professor; head of the department of fundamental and applied mathematics, faculty of mathematics and informatics

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Published

2019-11-27

Issue

No. 3 (2019): Journal of the Belarusian State University. Mathematics and Informatics

Section

Real, Complex and Functional Analysis

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How to Cite

[1]
Patseika, P.G. and Rouba , Y.A. 2019. Fejer means of rational Fourier – Chebyshev series and approximation of function |x|s. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Nov. 2019), 18–34. DOI:https://doi.org/10.33581/2520-6508-2019-3-18-34.