Abstract and Applied Analysis

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

Nimete Sh. Berisha, Faton M. Berisha, Mikhail K. Potapov, and Marjan Dema

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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.

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Abstr. Appl. Anal., Volume 2017 (2017), Article ID 9323181, 11 pages.

Received: 24 November 2016
Accepted: 19 January 2017
First available in Project Euclid: 12 April 2017

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Berisha, Nimete Sh.; Berisha, Faton M.; Potapov, Mikhail K.; Dema, Marjan. On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness. Abstr. Appl. Anal. 2017 (2017), Article ID 9323181, 11 pages. doi:10.1155/2017/9323181. https://projecteuclid.org/euclid.aaa/1491962538

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