S. B. Vakarchuk, A. V. Shvachko, “Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an “angle””, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 11,Pages <nobr>3

This article is cited in 10 papers

Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an “angle”

S. B. Vakarchuk^a, A. V. Shvachko^b

^a Chair of Economic Cybernetics and Mathematical Methods in Economy, Alfred Nobel University of Dnepropetrovsk, 18 Naberezhnaya Lenina str., Dnepropetrovsk, 49000 Unkraine
^b Chair of Higher Mathematics, Dnepropetrovsk State Agrarian-Economic University, 25 Voroshilov str., Dnepropetrovsk, 49600 Ukraine

Abstract: For functions of two variables we obtain sharp inequalities of Kolmogorov's type for partial and mixed intermediate derivatives. We also consider applications of the results to some problems of approximation of functions of two variables by angles and obtain a series of relations which are exact in definite sense.

Keywords: Hermite polynomials, Fourier–Hermite series, inequalities of Kolmogorov's type, the best approximation by angle, generalized polynomial.

UDC: 517.5

Received: 14.03.2014