2019
Том 71
№ 5

# Zhyhallo K. M.

Articles: 10
Article (Ukrainian)

### Approximative properties of biharmonic Poisson integrals on Hölder classes

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

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

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

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

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

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

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

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

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.