Approximation of 2π-periodic functions by Taylor—Abel—Poisson operators in the integral metric

J. Prestin; V.V. Savchuk; A.L. Shidlich

doi:10.15407/dopovidi2017.01.017

Approximation of 2π-periodic functions by Taylor—Abel—Poisson operators in the integral metric

Authors

J. Prestin Institute of Mathematics, University of Lübeck, Germany
V.V. Savchuk Institute of Mathematics of the NAS of Ukraine, Kiev
A.L. Shidlich Institute of Mathematics of the NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2017.01.017

Keywords:

direct approximation theorem, inverse approximation theorem, K-functional, linear approximation method

Abstract

We obtain direct and inverse approximation theorems of 2π-periodic functions by Taylor — Abel — Poisson operators in the integral metric.

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References

Savchuk V.V. Ukr. Math. J., 2007, 59, No 9: 1397-1407. https://doi.org/10.1007/s11253-007-0094-0

Savchuk V.V., Shidlich, A.L. Acta Sci. Math., 2014, 80, No 3-4: 477-489.

Leis R. Arch. Math., 1963, 14: 120-129. https://doi.org/10.1007/BF01234932

Butzer P.L., Sunouchi G. Math. Ann., 1964, 155: 316-330. https://doi.org/10.1007/BF01354864

Rudin W. Function theory in polydiscs, New York: Benjamin, 1969.

DeVore R.A., Lorentz G.G. Constructive approximation, Berlin: Springer, 1993. https://doi.org/10.1007/978-3-662-02888-9

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Published

22.05.2024

How to Cite

Prestin, J., Savchuk, V., & Shidlich, A. (2024). Approximation of 2π-periodic functions by Taylor—Abel—Poisson operators in the integral metric . Reports of the National Academy of Sciences of Ukraine, (1), 17–20. https://doi.org/10.15407/dopovidi2017.01.017