## Abstract and Applied Analysis

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

### 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

#### Abstract

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.

#### Article information

**Source**

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

**Dates**

Received: 24 November 2016

Accepted: 19 January 2017

First available in Project Euclid: 12 April 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1491962538

**Digital Object Identifier**

doi:10.1155/2017/9323181

**Mathematical Reviews number (MathSciNet)**

MR3630651

**Zentralblatt MATH identifier**

06929570

#### Citation

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