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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


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CiteScore 2017: 0.28
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2391-4661
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Volume 51, Issue 1

Issues

Pointwise approximation of 2 π/r-periodic functions by matrix operators of their Fourier series with r-differences of the entries

Włodzimierz Łenski
  • Corresponding author
  • University of Zielona Góra, Faculty of Mathematics, Computer Science and Econometrics, Zielona Góra, ul. Szafrana, Poland
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Bogdan Szal
  • University of Zielona Góra, Faculty of Mathematics, Computer Science and Econometrics, Zielona Góra, ul. Szafrana, Poland
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Published Online: 2018-12-05 | DOI: https://doi.org/10.1515/dema-2018-0024

Abstract

We extend the results of Xh. Z. Krasniqi [Acta Comment. Univ. Tartu. Math., 2013, 17, 89-101] and the authors [Acta Comment. Univ. Tartu. Math., 2009, 13, 11-24] to the case of 2 π/r-periodic functions. Moreover, as a measure of approximation r-differences of the entries are used.

Keywords: rate of approximation; summability of Fourier series

MSC 2010: 42A24

References

  • [1] Zygmund A., Trigonometric series, Cambridge, 2002Google Scholar

  • [2] Lenski W., Szal B., Approximation of functions belonging to the class Lp(ω) by linear operators, Acta Comment. Univ. Tartu. Math., 2009, 13, 11-24Google Scholar

  • [3] Krasniqi Xh. Z., Slight extensions of some theorems on the rate of pointwise approximation of functions from some subclasses of LpGoogle Scholar

  • [4] Szal B., On L-convergence of trigonometric series, J. Math. Anal. Appl., 2011, 373, 449-463Google Scholar

  • [5] Szal B., A new class of numerical sequences and its applications to uniform convergence of sine series, Math. Nachr., 2011, 284(14-15), 1985-2002.Web of ScienceGoogle Scholar

About the article

Received: 2018-05-24

Accepted: 2018-09-25

Published Online: 2018-12-05

Published in Print: 2018-11-01


Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 309–322, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0024.

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© by Włodzimierz Łenski, Bogdan Szal, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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