2019
Том 71
№ 4

All Issues

Hrabova U. Z.

Articles: 3
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

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)

Order Estimates for the Best Approximations and Approximations by Fourier Sums of the Classes of (ψ, β)-Differential Functions

Hrabova U. Z., Serdyuk A. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 9. - pp. 1186–1197

We establish exact-order estimates for the best uniform approximations by trigonometric polynomials on the classes C ψ β, p of 2π-periodic continuous functions f defined by the convolutions of functions that belong to the unit balls in the spaces L p , 1 ≤ p < ∞, with generating fixed kernels Ψβ ⊂ L p, \( \frac{1}{p}+\frac{1}{{p^{\prime}}}=1 \) , whose Fourier coefficients decrease to zero approximately as power functions. Exactorder estimates are also established in the L p -metric, 1 < p ≤ ∞, for the classes L ψ β,1 of 2π -periodic functions f equivalent in terms of the Lebesgue measure to the convolutions of kernels Ψβ ⊂ L p with functions from the unit ball in the space L 1. It is shown that, in the investigated cases, the orders of the best approximations are realized by Fourier sums.