2019
Том 71
№ 9

# Motornaya O. V.

Articles: 7
Article (Ukrainian)

### On the joint approximation of a function and its derivatives in the mean

Ukr. Mat. Zh. - 2019. - 71, № 2. - pp. 261-270

We consider some properties of functions integrable on a segment. Some estimates for the approximations of function and its derivatives are obtained.

Article (Russian)

### On the classification of functions integrable on a segment

Ukr. Mat. Zh. - 2016. - 68, № 5. - pp. 642-656

The problem of classification of functions integrable on a segment is considered. Estimates for the integral moduli of continuity of functions from generalized Potapov’s classes are obtained.

Article (Russian)

### Generalized Lebesgue Constants and the Convergence of Fourier–Jacobi Series in the Spaces $L_{1,A,B}$

Ukr. Mat. Zh. - 2014. - 66, № 2. - pp. 259–268

Generalized Lebesgue constants for the Fourier–Jacobi sums and the convergence of Fourier–Jacobi series in the $L_{1,A,B}$ spaces are investigated.

Article (Russian)

### One-sided approximation of a step by algebraic polynomials in the mean

Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 409–422

An asymptotically sharp estimate is obtained for the best one-sided approximation of a step by algebraic polynomials in the space $L_1$.

Article (Russian)

### Comparison theorems for some nonsymmetric classes of functions

Ukr. Mat. Zh. - 2008. - 60, № 7. - pp. 969–975

We prove comparison theorems of the Kolmogorov type for some nonsymmetric classes of functions.

Article (Russian)

### On asymptotically exact estimates for the approximation of certain classes of functions by algebraic polynomials

Ukr. Mat. Zh. - 2000. - 52, № 1. - pp. 85-99

We present a survey of results obtained for the last decade in the field of approximation of specific functions and classes of functions by algebraic polynomials in the spaces C and L 1 and approximation with regard for the location of a point on an interval.

Brief Communications (Russian)

### On the asymptotic estimates of the best approximations of differentiable functions by algebraić polynomials in the space $L_1$

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 859–862

An asymptotically exact estimate is obtained for the best approximations of $r$ times differentiable functions by algebraic polynomials in the space $L_1$.