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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 47, Issue 4

Issues

Approximation of Conjugate Functions by General Linear Operators of Their Fourier Series at the Lebesgue Points

Włodzimierz Łenski
  • UNIVERSITY OF ZIELONA GÓRA FACULTY OF MATHEMATICS, COMPUTER SCIENCE AND ECONOMETRICS ul. Szafrana 4a 65-516 ZIELONA GÓRA, POLAND
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/ Bogdan Szal
  • UNIVERSITY OF ZIELONA GÓRA FACULTY OF MATHEMATICS, COMPUTER SCIENCE AND ECONOMETRICS ul. Szafrana 4a 65-516 ZIELONA GÓRA, POLAND
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Published Online: 2014-12-11 | DOI: https://doi.org/10.2478/dema-2014-0071

Abstract

The pointwise estimates of the deviations r T͂n,A,Bf (·) - f͂͂ (·) and T͂n,A,Bf (·) - f͂͂ (·,ε) in terms of moduli of continuity ω̃f and r ω̃f are proved. Analogical results on norm approximation with remarks and corollary are also given. These results generalized a theorem of Mittal [3, Theorem 1, p. 437].

Keywords: and phrases rate of approximation; summability of Fourier series

References

  • [1] S. Aljancic, R. Bojanic, M. Tomic, On the degree of convergence of Fejér-Lebesgue sums, Enseign. Math., Geneva, 15 (1969), 21-28.Google Scholar

  • [2] W. Łenski, B. Szal, Approximation of integrable functions by general linear operators of their Fourier series at the Lebesgue points, Acta Math. Hungar. 131(4) (2011), 380-394.Web of ScienceGoogle Scholar

  • [3] M. L. Mittal, A sufficient condition for pF1q-effectiveness of the C1T-method, J. Math. Anal. Appl. 220 (1998), 434-450. Article no. AY975781 Google Scholar

  • [4] M. L. Mittal, B. E. Rhoades, V. N. Mishra, Approximation of signals (functions) belonging to the weighted W(Lp, ζ(t)); (p ≥ 1) -class by linear operators, Int. J. Math. Math. Sci., Vol. 2006, (2006), Article ID: 53538.Google Scholar

  • [5] A. Zygmund, Trigonometric Series, Cambridge, 2002. Google Scholar

About the article

Received: 2013-06-10

Revised: 2014-05-12

Published Online: 2014-12-11

Published in Print: 2014-12-01


Citation Information: Demonstratio Mathematica, Volume 47, Issue 4, Pages 878–892, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0071.

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© by Włodzimierz Łenski. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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