Abstract
The work focuses on the solution of a problem of approximation theory. The task is to investigate approximative properties of the Weierstrass integrals on the classes \( {W}_{\beta}^r{H}^{\alpha } \). We obtain asymptotic equalities for the upper borders of defluxion of functions from the classes \( {W}_{\beta}^r{H}^{\alpha } \) from the Weierstrass integrals.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. I. Stepanets, Methods of Approximation Theory. Part 1, VSP, Leiden, 2005.
Yu. I. Kharkevych and I. V. Kal’chuk, “Approximation of (ψ, β)–differentiable functions by Weierstrass integrals,” Ukr. Math. J., 59, No. 7, 1059–1087 (2007).
P. P. Korovkin, “On the best approximation of functions of class Z 2 by some linear operators,” Dokl. Akad. Nauk SSSR, 127, No. 3, 143–149 (2007).
L. I. Bausov, “Approximation of functions of class Z_ by positive methods of summation of Fourier series,” Uspekhi Mat. Nauk, 16, No. 3, 143–149 (1961).
L. P. Falaleev, “On approximation of functions by generalized Abel–Poisson operators,” Sib. Math. J., 42, No. 4, 779–788 (2001).
L. I. Bausov, “Linear methods of summing Fourier series with prescribed rectangular matrices. I,” Izv. Vyssh. Uchebn. Zaved. Mat., 3, 15–31 (1965).
V. A. Baskakov, “Some properties of operators of Abel–Poisson type,” Math. Notes, 17, No. 2, 101–107 (1975).
I. V. Kal’chuk, “Approximation of (ψ, β)–differentiable functions defined on the real axis by Weierstrass operators,” Ukr. Math. J., 59, No. 9, 1342–1363 (2007).
U. Z. Hrabova, I. V. Kal’chuk, and T. A. Stepaniuk, “ Approximation of functions from classes \( {W}_{\beta}^r{H}^{\alpha } \) by Weierstrass integrals,” Ukr. Math. J., 69, No. 4, 598–608 (2017).
Yu. I. Kharkevych and T. V. Zhyhallo, “Approximation of functions defined on the real axis by operators generated by λ–methods of summation of their Fourier integrals,” Ukr. Math. J., 56, No. 9, 1509–1525 (2004).
T. V. Zhyhallo and Yu. I. Kharkevych, “Approximation of (ψ, β)–differentiable functions defined on the real axis by Abel–Poisson operators,” Ukr. Math. J., 57, No. 8, 1297–1315 (2005).
I. V. Kal’chuk and Yu. I. Kharkevych, “Approximating properties of biharmonic Poisson integrals in the classes \( {W}_{\beta}^r{H}^{\alpha } \),” Ukr. Math. J., 68, No. 11, 1727–1740 (2017).
T. V. Zhyhallo and Yu. I. Kharkevych, “Approximation of (ψ, β)–differentiable functions by Poisson integrals in the uniform metric,” Ukr. Math. J., 61, No. 11, 1757–1779 (2009).
T. V. Zhyhallo and Yu. I. Kharkevych, “ Approximation of functions from the class \( {C}_{\beta}^{\psi } \) by Poisson integrals in the uniform metric,” Ukr. Math. J., 61, No. 12, 1893–1914 (2009).
Yu. I. Kharkevich and T. A. Stepanyuk, “Approximation properties of Poisson integrals for the classes \( {C}_{\beta}^{\psi }{H}^{\alpha } \),” Math. Notes, 96, No. 6, 1008–1019 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Ukrains’kiǐ Matematychnyǐ Visnyk, Vol. 14, No. 3, pp. 361–369 July–September, 2017.
Rights and permissions
About this article
Cite this article
Grabova, U.Z., Kal’chuk, I.V. & Stepaniuk, T.A. Approximative properties of the Weierstrass integrals on the classes \( {W}_{\beta}^r{H}^{\alpha } \). J Math Sci 231, 41–47 (2018). https://doi.org/10.1007/s10958-018-3804-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-018-3804-2