Approximative properties of the three-harmonic Poisson integrals on the classes $W^{r}_{\beta}H^{\alpha}$.-Reference-Cited by-同舟云学术

Approximative properties of the three-harmonic Poisson integrals on the classes $W^{r}_{\beta}H^{\alpha}$.

Published:2020-12-14 Issue:4 Volume:17 Page:538-548
ISSN:1810-3200
Container-title:Ukrainian Mathematical Bulletin
language:uk
Short-container-title:UMB

Author:

Hrabova Ulyana¹,Kal'chuk Inna¹,Filozof Leontii¹

Affiliation:

1. Lesya Ukrainka Volyn National University, Lutsk, Ukraine

Abstract

We obtained the asymptotic equalities for the least upper bounds of the approximation of functions from the classes $W^{r}_{\beta}H^{\alpha}$ by three-harmonic Poisson integrals in the case $r+\alpha\leq 3$ in the uniform metric.

Publisher

Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine

Reference19 articles.

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3. Baskakov, V. A. (1975). On some properties of operators of the Abel-Poisson type. Mat. Zametki, 17(2), 169-180.

4. Kaniev, S. (1963). On deviations of the functions biharmonic in a circle from their boundary values. Dokl. AN SSSR, 153(5), 995-998.

5. Hembars’ka, S.B. (2018). On boundary values of three-harmonic Poisson integral on the boundary of a unit disk. Ukr. Math. J., 70 (7), 1012–1021. https://doi.org/10.1007/s11253-018-1548-2

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