On some approximation properties of Gauss-Weierstrass singular operators

Author:

Shvai Olga1,Pozharska Kateryna2

Affiliation:

1. Lesya Ukrainka Volyn National University, Lutsk, Ukraine

2. Institute of Mathematics of the NAS of Ukraine, Kyiv, Ukraine

Abstract

Approximation theorems were formulated for function continuous in the neighborhood of some point $x$, $-\infty <x<\infty $. Namely, the upper bounds were obtained for the function approximations by their Gauss-Weierstrass singular operators in terms of a majorant function for the first- and second-order continuity moduli of the relevant functions.

Publisher

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

Reference17 articles.

1. Abdullayev, F.G., & Kharkevych, Yu.I. (2020). Approximation of the classes $C_{\beta}^{\psi}H^{\alpha}by biharmonic Poisson integrals. Ukr. Math. J., 72 (1), 21–38. https://doi.org/10.1007/s11253-020-01761-6

2. Baskakov, V.A. (1975). Some properties of operators of Abel-Poisson type. Math. Notes of the Academy of Sciences of the USSR, 17 (2), 101–107. https://doi.org/10.1007/bf01161864

3. Bugrov, Ja.S. (1963). Inequalities of the type of Bernstein inequalities and their application to the investigation of the differential properties of solutions of differential equations of higher order. Mathematica (Cluj), 5 (28), 7–25.

4. Falaleev, L.P. (2001). On approximation of functions by generalized Abel-Poisson operators. Sib. Math. J., 42 (4), 926–936.

5. Gradshtein, I.S., & Ryzhik, I.M. (1963). Tables of integrals, sums, series, and products. Fizmatgiz, Moscow (in Russian).

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