2019
Том 71
№ 11

# Zhyhallo T. V.

Articles: 6
Article (Ukrainian)

### On the approximation of functions from the Hölder class given on a segment by their biharmonic Poisson operators

Ukr. Mat. Zh. - 2019. - 71, № 7. - pp. 915-921

UDC 517.5
We obtain the exact equality for the upper bounds of deviations of biharmonic Poisson operators on the Hölder classes of functions continuous on the segment $[-1;1]$.

Article (Ukrainian)

### Approximating properties of biharmonic Poisson operators in the classes $\hat{L}^{\psi}_{\beta, 1}$

Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 650-656

We obtain the asymptotic equalities for the least upper bounds of the approximations of functions from the classes $\hat{L}^{\psi}_{\beta, 1}$ by biharmonic Poisson operators in the integral metric.

Article (Ukrainian)

### Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric

Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1497-1515

We obtain asymptotic equalities for upper bounds of approximations of functions from the class $C_{β,∞} ψ$ by Poisson integrals in the metric of the space $C$.

Article (Ukrainian)

### Approximation of functions from the class $\hat{C}^{\psi}_{\beta, \infty}$ by Poisson biharmonic operators in the uniform metric

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 669 – 693

We obtain asymptotic equalities for upper bounds of approximations of functions from the class $\hat{C}^{\psi}_{\beta, \infty}$ by the Poisson biharmonic operators in the uniform metric.

Article (Ukrainian)

### Approximation of $(\psi, \beta)$-Differentiable Functions Defined on the Real Axis by Abel-Poisson Operators

Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1097 – 1111

We obtain asymptotic equalities for upper bounds of approximations of functions on the classes $\hat C_{\beta ,\infty }^\psi$ and $\hat L_{\beta ,1}^\psi$ by Abel-Poisson operators.

Article (Ukrainian)

### Approximation of functions defined on the real axis by operators generated by λ-methods of summation of their Fourier integrals

Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1267-1280

We obtain asymptotic equalities for upper bounds of the deviations of operators generated by λ-methods (defined by a collection Λ={λσ(·)} of functions continuous on [0; ∞) and depending on a real parameter σ) on classes of (ψ, β)-differentiable functions defined on the real axis.