O. G. Rovenskaya, O. A. Novikov, “Approximation of the periodical functions of high smoothness by the right-angled linear means of Fourier series”, Computer Research and Modeling, 2012, Volume 4, Issue 3,Pages <nobr>521

This article is cited in 4 papers

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Approximation of the periodical functions of high smoothness by the right-angled linear means of Fourier series

O. G. Rovenskaya^a, O. A. Novikov^b

^a Donbass State Engineering Academy, 72 Shkadinova st., Kramatorsk, 84313, Ukraine
^b Slavyansk State Pedagogical University, 19 G. Batyuk st., Slavyansk, 84116, Ukraine

Abstract: We obtain asymptotic equalities for upper bounds of the deviations of the right-angled de la Vallee Poussin sums taken over classes of periodical functions of many variables of high smoothness. These equalities guarantee the solvability of the Kolmogorov–Nikol’skii problem for the right-angled de la Vallee Poussin sums on the specified classes of functions.

Keywords: ($\psi,\beta$)-derivative, the right-angled de la Vallee Poussin sums, Kolmogorov–Nikol'skiy problem.

UDC: 517.5

Received: 10.06.2012
Revised: 23.07.2012

DOI: 10.20537/2076-7633-2012-4-3-521-529