Approximation of classes of Poisson integrals by Fejer sums

Keywords: asymptotic equality; Poisson integrals; Fejer sums

Abstract

For upper bounds of the deviations of Fejer sums taken over classes of periodic functions that admit analytic extensions to a fixed strip of the complex plane, we obtain asymptotic equalities. In certain cases, these equalities give a solution of the corresponding Kolmogorov-Nikolsky problem.

Downloads

Download data is not yet available.

Author Biographies

O. O. Novikov, Donbass State Pedagogical University, Slov'yansk, 19 G. Batuka, 84116

Oleg Novikov. ResearcherID:  V-5638-2018 

O. G. Rovenska, Donbass State Engineering Academy, Kramatorsk, 72 Akademicheskaya, 84313

Olga Rovenska:  ResearcherID: V-5628-2018

Scopus Author ID: 57194348450

Yu. A. Kozachenko, Donbass State Pedagogical University, Slov'yansk, 19 G. Batuka, 84116

Yulia A. Kozachenko: ResearcherID:  V-6517-2018

 

References

A.I. Stepanec. Solution of the Kolmogorov-Nikol'skij problem for the Poisson integrals of continuous functions. Mat. Sb., 2001. - 192(1). - P. 113-138 (in Russian).

S.M. Nikolskiy. Approximation of the functions by trigonometric polynomials in the mean. Izv. Acad. Nauk. SSSR, Ser. Mat., 1946. -10(3). - P. 207-256 (in Russian).

S.B. Stechkin. Estimation of the remainder of Fourier series for the differentiable functions. Tr. Mat. Inst. Acad. Nauk SSSR. - 1980. - 145. - P. 126-151 (in Russian).

V.I. Rukasov, S.O. Chaichenko. Approximation of the classes of analytical functions by de la Vallee-Poussin sums. Ukr. Math. J. - 2002. - 54. - P. 2006-2024.

A.S. Serdyuk. Approximation of Poisson integrals by de la Vallee Poussin sums. Ukr. Math. J. - 2004. - 56. - P. 122-134.

V.V. Savchuk, M.V. Savchuk, S.O. Chaichenko. Approximation of analytic functions by de la Vallee Poussin sums. Mat. Stud. - 2010. - 34(2). - P. 207-219 (in Ukrainian).

O.O. Rovenska, O.O. Novikov. Approximation of Poisson integrals by repeated de la Vallee Poussin sums. Nonl. Oscil. - 2010. - 13. - P. 108-111.

V.E. Velichko, O.A. Novikov, O.G. Rovenskaya. V.I. Rukasov. Approximation of analytic functions by repeated de la Vallee Poussin sums. Tr. Inst. Prikl. Mat. Mekh. - 2011. - 22. - P. 33-42 (in Rusian).

O.A. Novikov, O.G. Rovenska. Approximation of classes of Poisson integrals by Fejer sums. Computer Research and Modeling. - 2015. - 7 (4). - P. 813-819 (in Russian).

O.O. Novikov, O.G. Rovenska, Yu.V. Kozachenko. Approximation of Poussin integrals by Fejer sums. Modern problems of probability theory and mathematical analysis. Scientific conference, Vorohta, 24-27 February, 2016, P. 110 (in Ukrainian).

O.G. Rovenska, O.O. Novikov. Approximation of analytic periodic functions by linear means of Fourier series. Cheb. Sb. - 2016. - 17 (2). - P. 170-183 (in Russian).

O.Novikov, O. Rovenska. Approximation of Classes of Poisson Integrals by Repeated Fejer Sums. Lobachevskii Journal of Mathematics. - 2017. -38. - P. 502-509.

O.O. Novikov, O.G. Rovenska. Approximation of periodic analytic functions by Fejer sums. Mat. Stud. - 2017. - 47. - P. 196-201.

A.I. Stepanec, Classication and Approximation of Periodic Functions. 1987. Naukova Dumka, Kiev, 268 p. (in Russian).

A.I. Stepanec, Classication and Approximation of Periodic Functions. 1995. Dordrecht, Kluwer, 393 p.

Published
2018-02-10
Cited
0 article
How to Cite
Novikov, O., Rovenska, O., & Kozachenko, Y. (2018). Approximation of classes of Poisson integrals by Fejer sums. Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, 87, 4-12. https://doi.org/10.26565/2221-5646-2018-87-01
Section
Статті