2019
Том 71
№ 7

All Issues

Kalchuk I. V.

Articles: 6
Article (Ukrainian)

On the approximation of the classes $W_{β}^rH^{α}$ by biharmonic Poisson integrals

Hrabova U. Z., Kalchuk I. V., Stepanyuk T. A.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 5. - pp. 625-634

We obtain asymptotic equalities for the least upper bounds of the deviations of biharmonic Poisson integrals from functions of the classes $W_{β}^rH^{α}$ in the case where $r > 2, 0 \leq \alpha < 1$.

Article (Ukrainian)

Approximation of functions from the classes $W_{β}^r H^{α }$ by Weierstrass integrals

Hrabova U. Z., Kalchuk I. V., Stepanyuk T. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 4. - pp. 510-519

We investigate the asymptotic behavior of the least upper bounds of the approximations of functions from the classes $W_{β}^r H^{α }$ by Weierstrass integrals in the uniform metric.

Article (Ukrainian)

I. Approximative properties of biharmonic Poisson integrals in the classes $W^r_{\beta} H^{\alpha}$

Kalchuk I. V., Kharkevych Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 11. - pp. 1493-1504

We deduce asymptotic equalities for the least upper bounds of approximations of functions from the classes $W^r_{\beta} H^{\alpha}$, and $H^{\alpha}$ by biharmonic Poisson integrals in the uniform metric.

Article (Ukrainian)

Approximation of ( ψ, β )-differentiable functions defined on the real axis by Weierstrass operators

Kalchuk I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1201–1220

Asymptotic equalities are obtained for upper bounds of approximations by the Weierstrass operators on the functional classes $\widehat{C}^{\psi}_{\beta, \infty}$ and $\widehat{L}^{\psi}_{\beta, 1}$ in metrics of the spaces $\widehat{C}$ and $\widehat{L}_1$, respectively.

Article (Russian)

Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals

Kalchuk I. V., Kharkevych Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1105–1115

Complete asymptotic decompositions are obtained for values of exact upper bounds of approximations of functions from the classes $W^r_1,\quad r \in N,$ and WJr, $\overline{W}^r_1,\quad r \in N\backslash\{1\}$, by their biharmonic Poisson integrals.

Article (Ukrainian)

Approximation of (ψ, β)-differentiable functions by Weierstrass integrals

Kalchuk I. V., Kharkevych Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 7. - pp. 953–978

Asymptotic equalities are obtained for upper bounds of approximations of functions from the classes $C^{\psi}_{\beta \infty}$ and $L^{\psi}_{\beta 1}$ by the Weierstrass integrals.