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On the Rate of Approximation by Generalized de la Vallée Poussin Type Matrix Transform Means of Walsh-Fourier Series

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Abstract

In this paper, we consider norm convergence issues for matrix-based de la Vallée Poussin-like means of Fourier series for the Walsh system. In the main theorem of the paper, we state a proposition that estimates the difference between the named means above and the corresponding function in norm. The upper estimation is given by and as a function of the modulus of continuity of the function.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Sciences, University of Nyíregyháza, H-4400, Sóstói street 31/b, Nyíregyháza, Hungary

    I. Blahota

  2. Institute of Mathematics, University of Debrecen, Pf. 400, Debrecen, 4002, Hungary

    G. Gát

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  1. I. Blahota
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  2. G. Gát
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Correspondence to I. Blahota or G. Gát.

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Blahota, I., Gát, G. On the Rate of Approximation by Generalized de la Vallée Poussin Type Matrix Transform Means of Walsh-Fourier Series. P-Adic Num Ultrametr Anal Appl 14 (Suppl 1), S59–S73 (2022). https://doi.org/10.1134/S2070046622050053

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  • DOI: https://doi.org/10.1134/S2070046622050053

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