Skip to main content
SpringerLink
Log in

Approximation of integrable functions by general linear operators of their fourier series

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

The pointwise estimates of the deviation T n,A,B f(·)−f(·) in terms of moduli of continuity −w·f and w·f there are proved. Analogical results on norm approximation with remarks and corollaries are also given. In the results there are used the essentially weaker conditions than these in [Mittal, M. L.: J. Math. Anal. Appl., 220, 434–450 (1998) Theorem 1, p. 437].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Mittal, M. L.: A sufficient condition for F-effectiveness of the C 1 T-method. J. Math. Anal. Appl., 220, 434–450 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Gát, G., Goginava, U.: On the divergence of Nörlund logarithmic means of Walsh-Fourier series. Acta Mathematica Sinica, English Series, 25(6), 903–916 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Łenski, W.: On the rate of pointwise summability of Fourier series. Appl. Math. E-Notes, 1, 143–148 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Taberski, R.: On the convergence of singular integrals (in Polish). Zeszyty Nauk. Uniw. Mickiewicza, 25, 33–51 (1960)

    MathSciNet  Google Scholar 

  5. Zygmund, A.: Trigonometric Series, Cambridge University Press, Cambridge, 2002

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, 65-516, Zielona Góra, ul. Szafrana 4a, Poland

    Włodzimierz Łenski & Bogdan Szal

Authors
  1. Włodzimierz Łenski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bogdan Szal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Włodzimierz Łenski.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Łenski, W., Szal, B. Approximation of integrable functions by general linear operators of their fourier series. Acta. Math. Sin.-English Ser. 28, 1119–1134 (2012). https://doi.org/10.1007/s10114-011-0568-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-011-0568-8

Keywords

MR(2000) Subject Classification

Search

Navigation