2019
Том 71
№ 11

# Vakarchuk B. S.

Articles: 4
Article (Russian)

### Jackson-type inequalities with generalized modulus of continuity and exact values of the $n$-widths for the classes of $(ψ,β)$-differentiable functions in $L_2$. III

Ukr. Mat. Zh. - 2016. - 68, № 10. - pp. 1299-1319

In the classes $L^{\psi}_{\beta ,2}$ of $2\pi$ -periodic $(\psi , \beta)$-differentiable functions for which $f^{\psi}_{\beta} \in L_2$, we determine the exact constants in Jackson-type inequalities for the characteristic of smoothness $\Lambda_{\gamma} (f, t) = \biggl\{\frac1t \int^t_0 \| \Delta^{\gamma}_ h(f)\|^2dh \biggr\}^{1/2}$, $t > 0$, deternined by averaging the norm of the generalized difference relation $\Delta_{ \gamma}h(f)$. For the classes of $(\psi,\beta)$ -differentiable functions defined by using the characteristic of smoothness $\Lambda_{\gamma}$ and the majorant $\Phi$, satisfying numerous conditions, we find the exact values of some $n$-widths in $L_2$.

Brief Communications (Russian)

### Darbou's tensor and surfaces of the second order in a Lobachevsky space

Ukr. Mat. Zh. - 1964. - 16, № 5. - pp. 671-675

Brief Communications (Russian)

### On mapping of Clifford curves and surfaces in an elliptical space

Ukr. Mat. Zh. - 1964. - 16, № 4. - pp. 521-528

Brief Communications (Russian)

### On Spherical Representation of Curves and Surfaces in a Lobachevsky Space

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 87-92