Abstract
Asymptotic equalities have been obtained for the exact upper bounds of the deviations of threeharmonic Poisson integrals in the uniform metric on the classes of continuous (ψ, β)-differentiable functions of low smoothness. The established equalities give a solution of the Kolmogorov–Nikolskii problem for three-harmonic Poisson integrals on the classes \( {C}_{\beta, \infty}^{\psi } \) in the uniform metric.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 19, No. 3, pp. 355–372, July–September, 2022.
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Hrabova, U.Z., Kal’chuk, I.V. Approximation of Classes \( {C}_{\beta, \infty}^{\psi } \) by Three-Harmonic Poisson Integrals in Uniform Metric (Low Smoothness). J Math Sci 268, 178–191 (2022). https://doi.org/10.1007/s10958-022-06190-3
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DOI: https://doi.org/10.1007/s10958-022-06190-3