2019
Том 71
№ 6

# Polyakov O. V.

Articles: 7
Brief Communications (Russian)

### On the Best (α;β)-Approximations of Convex Functions by Constants in Integral Metrics

Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 1015–1020

We prove inequalities connecting the constants of the best (α;β) -approximation in the space L p for various values of p.

Brief Communications (Russian)

### On rational functions of the best nonsymmetric approximations in integral metrics

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1575-1577

We obtain theorems that characterize the degree of the rational function of the best $(\alpha, \beta)$ -approximation in the space $L_p$ and conditions under which the value of the best rational $(\alpha, \beta)$ -approximation is less than the best $(\alpha, \beta)$ -approximation by algebraic polynomials.

Brief Communications (Ukrainian)

### Best cubature formulas for some classes of continuous functions of two variables

Ukr. Mat. Zh. - 2009. - 61, № 4. - pp. 572-576

The exact value of the error of a cubature formula is determined for some classes of continuous functions of two variables defined by strictly monotone moduli of continuity.

Article (Russian)

### Asymmetric approximations in the space $L_{p(t)}$

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 952-959

We introduce the notion of $(α,β)$-norm in the space $L_{p(t)}$ of functions $x(t)$ for which $$\int\limits_0^1 {\left| {x(t)} \right|^{p(t)}< \infty }$$ where $p(t)$ is a positive measurable function. We establish a criterion for the element of the best $(α,β)$-approximation in the space $L_{p(t)}$. We obtain inequalities of the type of duality relations.

Brief Communications (Russian)

### On the best quadrature formulas for some classes of continuous functions

Ukr. Mat. Zh. - 1998. - 50, № 9. - pp. 1284–1288

We obtain the best quadrature formulas for classes of continuous functions defined by various restrictions on the moduli of continuity with respect to increase and decrease.

Brief Communications (Russian)

### On inequalities for seminorms of certain classes of differentiable periodic functions

Ukr. Mat. Zh. - 1997. - 49, № 10. - pp. 1432–1435

We obtained the inequalities for upper bounds of seminorms of classes of 2π-periodic functions, which are determined by a linear differential operator and by the majorant of the modulus of continuity.

Article (Ukrainian)

### Approximation of certain classes of differentiable functions by generalized splines

Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 951–957

We find the exnet value of the best (α, β)-approximation by generalized Chebyshev splines for a class of functions differentiable with weight on [−1, 1].