2018
Том 70
№ 9

All Issues

Sokolenko I. V.

Articles: 6
Anniversaries (Ukrainian)

Oleksandr Ivanovych Stepanets’ (on his 75th birthday)

Romanyuk A. S., Romanyuk V. S., Samoilenko A. M., Savchuk V. V., Serdyuk A. S., Sokolenko I. V.

Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 579

Chronicles (Ukrainian)

International conference "Theory of approximation of functions and its applications" dedicated to the 70 th birthday of the corresponding member of NASU Professor O. I. Stepanets (1942 - 2007)

Romanyuk A. S., Samoilenko A. M., Serdyuk A. S., Sokolenko I. V.

Ukr. Mat. Zh. - 2012. - 64, № 10. - pp. 1438-1440

Article (Ukrainian)

Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $H_{ω_p}$ in the metrics of the spaces $L_p$

Serdyuk A. S., Sokolenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 979–996

We obtain upper estimates for the least upper bounds of approximations of the classes of Poisson integrals of functions from $H_{ω_p}$ for $1 ≤ p < ∞$ by a certain linear method $U_n^{*}$ in the metric of the space $L_p$. It is shown that the obtained estimates are asymptotically exact for $р = 1$: In addition, we determine the asymptotic equalities for the best approximations of the classes of Poisson integrals of functions from $H_{ω_1}$ in the metric of the space $L_1$ and show that, for these classes, the method $U_n^{*}$ is the best polynomial approximation method in a sense of strong asymptotic behavior.

Chronicles (Ukrainian)

International Conference "Mathematical Analysis and Differential Equations and Applications"

Samoilenko A. M., Savchuk V. V., Sokolenko I. V., Stepanets O. I.

Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 431

Article (Ukrainian)

Approximation of the $\bar {\Psi}$ -integrals of functions defined on the real axis by Fourier operators

Sokolenko I. V., Stepanets O. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 7. - pp. 960–965

We find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by $\bar {\Psi}$-integrals. On these classes, we also obtain asymptotic equalities for the upper bounds of functionals that characterize the simultaneous approximation of several functions.

Article (Ukrainian)

Approximation of $\bar {\omega}$ -integrals of continuous functions defined on the real axis by Fourier operators

Sokolenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 5. - pp. 663-676

We obtain asymptotic formulas for the deviations of Fourier operators on the classes of continuous functions $C^{ψ}_{∞}$ and $\hat{C}^{\bar{\psi} } H_{\omega}$ in the uniform metric. We also establish asymptotic laws of decrease of functionals characterizing the problem of the simultaneous approximation of $\bar{\psi}$-integrals of continuous functions by Fourier operators in the uniform metric.