2019
Том 71
№ 11

# Motornyi V. P.

Articles: 22
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 exact constants in Hardy – Littlewood inequalities

Ukr. Mat. Zh. - 2017. - 69, № 12. - pp. 1625-1632

We obtain the exact constants for the Hardy – Littlewood inequalities.

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.

Anniversaries (Ukrainian)

### Major Pylypovych Timan (on his 90th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 8. - pp. 1141-1144

Anniversaries (Ukrainian)

### Oleksandr Ivanovych Stepanets’ (on the 70 th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 579-581

Article (Russian)

### Estimates for the best asymmetric approximations of asymmetric classes of functions

Ukr. Mat. Zh. - 2011. - 63, № 6. - pp. 798-808

Asymptotically sharp estimates are obtained for the best $(\alpha, \beta)$ -approximations of the classes $W^r_{1; \gamma, \delta}$ with natural $r$ by algebraic polynomials in the mean.

Article (Russian)

### On the mean convergence of Fourier–Jacobi series

Ukr. Mat. Zh. - 2010. - 62, № 6. - pp. 814–828

The convergence of Fourier–Jacobi series in the spaces $L_{p,A,B}$ is studied in the case where the Lebesgue constants are unbounded.

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)

### On the problem of approximation of functions by algebraic polynomials with regard for the location of a point on a segment

Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1087–1098

We obtain a correction of an estimate of the approximation of functions from the class W r H ω (here, ω(t) is a convex modulus of continuity such that tω '(t) does not decrease) by algebraic polynomials with regard for the location of a point on an interval.

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 One-Sided Approximation of Functions with Regard for the Location of a Point on an Interval

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 666-669

We investigate a pointwise approximation of functions of the class H ω (ω(t) is a modulus of continuity convex upward) by absolutely continuous functions with variable smoothness.

Article (Russian)

### On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials

Ukr. Mat. Zh. - 2001. - 53, № 6. - pp. 783-799

We obtain estimates for the approximation of functions of the class W r H ω, where ω(t) is a convex modulus of continuity such that tω′(t) does not decrease, by algebraic polynomials with regard for the position of a point on the segment [−1, 1]. The estimates obtained cannot be improved for all moduli of continuity simultaneously.

Article (Russian)

### Approximation of Certain Classes of Singular Integrals by Algebraic Polynomials

Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 331-345

We study the problem of pointwise approximation by algebraic polynomials for classes of functions that are singular integrals of bounded functions. We obtain asymptotically exact estimates of approximations.

Article (Russian)

### On the 80th birthday of Academician N. P. Korneichuk

Ukr. Mat. Zh. - 2000. - 52, № 1. - pp. 3-4

Article (Russian)

### On the results of N. P. Korneichuk obtained in 1990–1999

Ukr. Mat. Zh. - 2000. - 52, № 1. - pp. 5-8

We present a brief survey of Korneichuk’s works published in 1990–1999.

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.

Article (Russian)

### Approximation of fractional-order integrals by algebraic polynomials. II

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 940–951

We investigate the approximation of functions that are fractional-order integrals of bounded functions by algebraic polynomials.

Article (Russian)

### Approximation of fractional-order integrals by algebraic polynomials. I

Ukr. Mat. Zh. - 1999. - 51, № 5. - pp. 603–613

For functionsf(x) representable by an integral operator of a special form, we investigate the behavior of the second difference Δ h 2 f(x)=f(x+h)-2f(x)+f(x-h),h>0, depending on the location of a pointx on the segment [0,1].

Article (Russian)

### On quadrature formulas with equal coefficients

Ukr. Mat. Zh. - 1995. - 47, № 9. - pp. 1217–1223

For the Lipschitz classes, we obtain weight quadrature formulas asymptotically optimal with respect to coefficients.

Article (Ukrainian)

### Approximation of periodic functions by interpolation polynomials in L1

Ukr. Mat. Zh. - 1990. - 42, № 6. - pp. 781–786

Article (Ukrainian)

### Investigation of the optimization of quadrature formulas by Dnepropetrovsk mathematicians

Ukr. Mat. Zh. - 1990. - 42, № 1. - pp. 18–33