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Acta Mathematica Hungarica

, Volume 131, Issue 4, pp 380–394 | Cite as

Approximation of integrable functions by general linear operators of their Fourier series at the Lebesgue points

  • Włodzimierz ŁenskiEmail author
  • Bogdan Szal
Article
  • 48 Downloads

Abstract

Pointwise estimates of the deviation T n,A,B f(⋅)−f(⋅) in terms of moduli of continuity \(\bar{w}_{\cdot}f\) and w f are proved. Analog results on norm approximation with remarks and corollaries are also given. In the results essentially weaker conditions than those in [2, Theorem 1, p. 437] are used.

Key words and phrases

rate of approximation summability of Fourier series 

2000 Mathematics Subject Classification

42A24 

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References

  1. [1]
    S. Aljančič, R. Bojanic and M. Tomić, On the degree of convergence of Fejér–Lebesgue sums, L’Enseignement Mathematique, Geneva, XV (1969), 21–28. Google Scholar
  2. [2]
    M. L. Mittal, A sufficient condition for F.-effectiveness of the C 1 T-method, J. Math. Anal. Appl., 220 (1998), 434–450. MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    A. Zygmund, Trigonometric Series (Cambridge, 2002). zbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics, Computer Science and EconometricsUniversity of Zielona GóraZielona GóraPoland

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