2019
Том 71
№ 11

All Issues

Polyakov O. V.

Articles: 7
Brief Communications (Russian)

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

Polyakov O. V.

↓ Abstract   |   Full text (.pdf)

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

Polyakov O. V., Ruchaevskaya N. O.

↓ Abstract   |   Full text (.pdf)

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

Polyakov O. V., Polyakova N. O.

↓ Abstract   |   Full text (.pdf)

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 $L_{p(t)}$

Litvin E. G., Polyakov O. V.

↓ Abstract   |   Full text (.pdf)

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

Polyakov O. V.

↓ Abstract   |   Full text (.pdf)

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

Polyakov O. V.

↓ Abstract   |   Full text (.pdf)

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

Polyakov O. V.

↓ Abstract   |   Full text (.pdf)

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].