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Approximation of continuous functions given on the real axis by three-harmonic Poisson operators

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Approximation properties of three-harmonic Poisson operators on the classes of (ψ, β)-differentiable functions of low smoothness given on the real axis have been studied. Asymptotic equalities have been obtained that provide in some cases a solution to the Kolmogorov–Nikol’skii problem for three-harmonic Poisson operators P3,σ(f; x) on the classes \({\widehat{C}}_{\beta ,\infty }^{\psi },\beta \in {\mathbb{R}},\) in the uniform metric.

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Authors and Affiliations

  1. Lesya Ukrainka Volyn National University, Lutsk, Ukraine

    Ulyana Z. Hrabova & Inna V. Kal’chuk

Authors
  1. Ulyana Z. Hrabova
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  2. Inna V. Kal’chuk
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Correspondence to Ulyana Z. Hrabova.

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Presented by V. P. Motorny

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 20, No. 2, pp. 186–202, April–June, 2023

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Hrabova, U.Z., Kal’chuk, I.V. Approximation of continuous functions given on the real axis by three-harmonic Poisson operators. J Math Sci 274, 327–339 (2023). https://doi.org/10.1007/s10958-023-06603-x

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