2018
Том 70
№ 8

All Issues

Motornyi V. P.

Articles: 20
Article (Russian)

On the exact constants in Hardy – Littlewood inequalities

Motornyi V. P.

↓ Abstract

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

Motornaya O. V., Motornyi V. P., Sedunova V. V.

↓ Abstract

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 $L_{1,A,B}$

Motornaya O. V., Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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)

Babenko V. F., Motornyi V. P., Peleshenko B. I., Romanyuk A. S., Samoilenko A. M., Serdyuk A. S., Trigub R. M., Vakarchuk S. B.

Full text (.pdf)

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

Anniversaries (Ukrainian)

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

Gorbachuk M. L., Lukovsky I. O., Makarov V. L., Motornyi V. P., Romanyuk A. S., Samoilenko A. M., Serdyuk A. S., Sharko V. V., Zaderei P. V.

Full text (.pdf)

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

Article (Russian)

Estimates for the best asymmetric approximations of asymmetric classes of functions

Motornyi V. P., Pas'ko A. N.

↓ Abstract   |   Full text (.pdf)

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

Goncharov S. V., Motornyi V. P., Nitiema P. K.

↓ Abstract   |   Full text (.pdf)

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

Motornaya O. V., Motornyi V. P., Nitiema P. K.

↓ Abstract   |   Full text (.pdf)

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

Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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

Motornaya O. V., Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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

Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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

Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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

Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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

Babenko V. F., Ligun A. A., Mitropolskiy Yu. A., Motornyi V. P., Nikol'skii S. M., Samoilenko A. M.

Full text (.pdf)

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

Article (Russian)

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

Babenko V. F., Ligun A. A., Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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

Motornaya O. V., Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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

Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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

Motornyi V. P.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

Approximation of periodic functions by interpolation polynomials in L1

Motornyi V. P.

Full text (.pdf)

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

Article (Ukrainian)

Investigation of the optimization of quadrature formulas by Dnepropetrovsk mathematicians

Motornyi V. P.

Full text (.pdf)

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