Table of Contents
ISRN Mathematical Analysis
Volume 2014, Article ID 165389, 11 pages
http://dx.doi.org/10.1155/2014/165389
Research Article

Uniform Approximation of Periodical Functions by Trigonometric Sums of Special Type

Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs’ka Street, Kiev 01601, Ukraine

Received 12 November 2013; Accepted 1 December 2013; Published 5 January 2014

Academic Editors: G. Mantica and G. Ólafsson

Copyright © 2014 A. S. Serdyuk and Ie. Yu. Ovsii. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The approximation characteristics of trigonometric sums of special type on the class of ()-differentiable (in the sense of A. I. Stepanets) periodical functions are studied. Because of agreement between parameters of approximative sums and approximated classes, the solution of Kolmogorov-Nikol’skii problem is obtained in a sufficiently general case. It is shown that in a number of important cases these sums provide higher order of approximation in comparison with Fourier sums, de la Vallée Poussin sums, and others on the class in the uniform metric. The range of parameters in which the sums give the order of the best uniform approximation on the classes is indicated.