O. A. Novikov, O. G. Rovenskaya, “Approximation of the periodical functions of hight smoothness by the right-angled linear methods”, Computer Research and Modeling, 2011, Volume 3, Issue 3,Pages <nobr>255

This article is cited in 1 paper

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Approximation of the periodical functions of hight smoothness by the right-angled linear methods

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

^a Slavyansk State Pedagogical University, G. Batyuk st. 19, Slavyansk, 84116, Ukraine
^b Donbass State Engineering Academy, Shkadinova st. 72, Kramatorsk, 84313, 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 two 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: 25.05.2011

DOI: 10.20537/2076-7633-2011-3-3-255-264