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Abstract and Applied Analysis
Volume 2017, Article ID 9323181, 11 pages
Research Article

On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness

1Faculty of Economics, University of Prishtina, Nëna Terezë 5, Prishtina, Kosovo
2Faculty of Mathematics and Sciences, University of Prishtina, Prishtina, Kosovo
3Department of Mechanics and Mathematics, Moscow State University, Moscow 117234, Russia
4Faculty of Electrical and Computer Engineering, University of Prishtina, Prishtina, Kosovo

Correspondence should be addressed to Faton M. Berisha; ude.rp-inu@ahsireb.notaf

Received 24 November 2016; Accepted 19 January 2017; Published 21 March 2017

Academic Editor: Alberto Fiorenza

Copyright © 2017 Nimete Sh. Berisha et al. 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.


In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities.