2019
Том 71
№ 11

# Skorokhodov D. S.

Articles: 5
Article (Russian)

### On the Best Linear Approximation Method for Hölder Classes

Ukr. Mat. Zh. - 2015. - 67, № 9. - pp. 1265-1284

We find the exact values of one-dimensional linear widths for the Hölder classes of functions in the space C and the value of the best approximation of the Hölder classes of functions by a wide class of linear positive methods.

Article (English)

### On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 508-524

We study the following modification of the Landau-Kolmogorov problem: Let $k, r \in \mathbb{N}, \quad 1 \leq k \leq r -1$ and $p, q, s \in [1, \infty]$. Also let $MM^m,\; m \in \mathbb{N}$, be the class of nonnegative functions defined on the segment $[0,1]$ whose derivatives of orders $1, 2,... , m$ are nonnegative almost everywhere on $[0,1]$. For every $\delta > 0$, find the exact value of the quantity $$w^{k, r}_{p, q, s}(\delta; MM^m) := \sup \left\{ ||x^{(k)}||_q : \; x \in MM^m,\; ||x||_p \leq \delta, \;\; ||x^{(r)}||_s \leq 1\right\}$$ We determine the quantity $w^{k, r}_{p, q, s}(\delta; MM^m)$ in the case where $s = \infty$ and $m \in \{r,\; r — 1,\; r — 2\}$. In addition, we consider certain generalizations of the above-stated modification of the Landau-Kolmogorov problem.

Article (Russian)

### Landau-Kolmogorov problem for a class of functions absolutely monotone on a finite interval

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 531-548

We solve the Landau - Kolmogorov problem for the class of functions absolutely monotone on a finite interval. For this class of functions, a new exact additive inequalities of the Kolmogorov type are obtained.

Article (Russian)

### On the existence of a generalized asymmetric (α, β)-spline whose average values have equal minima at given points

Ukr. Mat. Zh. - 2009. - 61, № 2. - pp. 261-267

We solve the problem of existence of an asymmetric spline averaged in Steklov’s sense that takes equal minimum values at given points.

Article (Russian)

### On Kolmogorov-type inequalities for functions defined on a semiaxis

Ukr. Mat. Zh. - 2007. - 59, № 10. - pp. 1299–1312

Necessary and sufficient conditions for the existence of a function from the class S - with prescribed values of integral norms of three successive derivatives (generally speaking, of a fractional order) are obtained.