2018
Том 70
№ 8

All Issues

Zhyhallo K. M.

Articles: 10
Article (Ukrainian)

Approximative properties of biharmonic Poisson integrals on Hölder classes

Hembars'ka S. B., Zhyhallo K. M.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 7. - pp. 925-932

We establish asymptotic expansions for the values of approximation of functions from the H¨older class by biharmonic Poisson integrals in the uniform and integral metrics.

Article (Ukrainian)

Approximation of (ψ, β)-differentiable functions of low smoothness by biharmonic Poisson integrals

Kharkevych Yu. I., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 12. - pp. 1602-1622

We solve the Kolmogorov – Nikol’skii problem for biharmonic Poisson integrals on the classes of (ψ, β)- differentiable periodic functions of low smoothness in the uniform metric.

Article (Ukrainian)

Approximation of functions from the classes $C^{\psi}_{\beta, \infty}$ by biharmonic Poisson integrals

Kharkevych Yu. I., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 939-959

Asymptotic equalities are obtained for upper bounds of deviations of biharmonic Poisson integrals on the classes of $(\psi, \beta)$-differentiable periodic functions in the uniform metric.

Article (Ukrainian)

Approximation of conjugate differentiable functions by biharmonic Poisson integrals

Kharkevych Yu. I., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 3. - pp. 333-345

We determine the exact values of upper bounds of approximations by biharmonic Poisson integrals on classes of conjugate differentiable functions in uniform and integral metrics.

Article (Ukrainian)

Approximation of conjugate differentiable functions by their Abel–Poisson integrals

Kharkevych Yu. I., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 73-82

We obtain the exact values of upper bounds of approximations of classes of periodic conjugate differentiable functions by their Abel–Poisson integrals in uniform and integral metrics.

Article (Ukrainian)

Approximation of Differentiable Periodic Functions by Their Biharmonic Poisson Integrals

Kharkevych Yu. I., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1213-1219

We determine the exact values and asymptotic decompositions of upper bounds of approximations by biharmonic Poisson integrals on classes of periodic differentiable functions.

Article (Ukrainian)

Complete Asymptotics of the Deviation of a Class of Differentiable Functions from the Set of Their Harmonic Poisson Integrals

Kharkevych Yu. I., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 1. - pp. 43-52

On a class of differentiable functions W r and the class \(\overline W ^r \) of functions conjugate to them, we obtain a complete asymptotic expansion of the upper bounds \(\mathcal{E}(\mathfrak{N},A\rho )_C \) of deviations of the harmonic Poisson integrals of the functions considered.

Brief Communications (Ukrainian)

On the Approximation of Functions of the Hölder Class by Triharmonic Poisson Integrals

Kharkevych Yu. I., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 6. - pp. 855-859

We determine the exact value of the upper bound for the deviation of the triharmonic Poisson integral from functions of the Hölder class.

Brief Communications (Ukrainian)

On the Approximation of Functions of the Hölder Class by Biharmonic Poisson Integrals

Kharkevych Yu. I., Zhyhallo K. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 971-974

We determine the exact value of the upper bound of the deviation of biharmonic Poisson integrals from functions of the Hölder class.