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Approximation by Marcinkiewicz-Type Matrix Transform of Vilenkin–Fourier Series

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Abstract

In the present paper, we discuss the rate of the approximation by Marcinkiewicz-type matrix transform of Vilenkin–Fourier series in \(L^p(G^2_m)\) spaces (\(1\le p <\infty \)) and in \(C(G^2_m)\). Moreover, we give an application for functions in Lipschitz classes \(\text {Lip}(\alpha ,p,G_m^2)\) (\(\alpha >0,\ 1\le p <\infty \)) and \(\text {Lip}(\alpha ,C(G_m^2))\) (\(\alpha >0 \)).

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Authors and Affiliations

  1. Institute of Mathematics and Computer Sciences, University of Nyíregyháza, P.O.B. 166 , Nyíregyháza, 4400, Hungary

    István Blahota

  2. Institute of Mathematics and Computer Sciences, Eszterházy Károly Catholic University, Leányka street 4., Eger, 3300, Hungary

    Károly Nagy

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  1. István Blahota
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  2. Károly Nagy
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Correspondence to István Blahota.

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Blahota, I., Nagy, K. Approximation by Marcinkiewicz-Type Matrix Transform of Vilenkin–Fourier Series. Mediterr. J. Math. 19, 165 (2022). https://doi.org/10.1007/s00009-022-02105-3

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