ON ESTIMATION OF FOURIER AND QUASI-MONOTONE-FOURIER COEFFICIENTS OF FUNCTIONS IN NIKOL’SKII CLASSES

Authors

DOI:

https://doi.org/10.37560/matbil1190079r

Keywords:

Nikol'skii class, quasi-monotone coefficient, best approximation, modulus of smoothness

Abstract

An equivalent form of Nikol'skii class \(H(p,k,\varphi)\), \(p \in [1,\infty]\), using a supplementary condition for function \(\varphi\) and best approximation is given. The estimation of Fourier coefficients of functions belonging to the class \(H(p,k,\varphi)\), \(p \in [1,\infty]\), by means of best approximation and modulus of smoothness without giving supplementary conditions to the \(\varphi\) function is investigated. We discuss the problem for the functions with quasi-monotone Fourier coefficients as well.

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Published

2019-01-01

Issue

Vol. 43 No. 1 (2019): 43 (LXIX) 1 (2019)

Section

Articles

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Copyright (c) 2019 Matematichki Bilten

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
S. Rexhepi, S. Kera, and H. Snopce, “ON ESTIMATION OF FOURIER AND QUASI-MONOTONE-FOURIER COEFFICIENTS OF FUNCTIONS IN NIKOL’SKII CLASSES”, Mat. Bilt., vol. 43, no. 1, pp. 79–89, Jan. 2019, doi: 10.37560/matbil1190079r.