# Estimates of the best approximations of functions with a spectrum with a given majorant

### Abstract

Assessment of the best approximations of functions through its modulus of smoothness (direct theorems of approximation theory or theorems of Jackson type) and of modulus of smoothness through its best approximation in a given metric (inverse theorems of approximation theory or theorems similar to Bernstein's theorem) by orthogonal systems have been the subject of research of many generations of mathematicians. The relevance of this topic is determined by the numerical analysis, particularly with the development of computer technology. This topic is naturally linked to the further development of the tasks aiming to estimate the closestapproximation of a function, approximation of inequalities of Bernstein and Nikolskiy, and of approximation theory [1-8].

Published

Jun 27, 2016

How to Cite

EMBERGENOVA, Zh. K.; SIKHOV, M. B..
Estimates of the best approximations of functions with a spectrum with a given majorant.

**International Journal of Mathematics and Physics**, [S.l.], v. 7, n. 1, p. 21-26, june 2016. ISSN 2409-5508. Available at: <http://ijmph.kaznu.kz/index.php/kaznu/article/view/155>. Date accessed: 21 mar. 2019.
Section

Informatics and Mathematical Modeling

### Keywords

the best approximation, assessment of the best approximation, modulus of continuity