2018
Том 70
№ 8

All Issues

Babenko V. V.

Articles: 4
Article (Russian)

Approximation of some classes of set-valued periodic functions by generalized trigonometric polynomials

Babenko V. F., Babenko V. V., Polishchuk M. V.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 449-459

We generalize some known results on the best, best linear, and best one-sided approximations by trigonometric polynomials from the classes of $2 \pi$ -periodic functions presented in the form of convolutions to the case of classes of set-valued functions.

Article (English)

On the Optimal Recovery of Integrals of Set-Valued Functions

Babenko V. F., Babenko V. V., Polishchuk M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 9. - pp. 1163-1171

We consider the problem of optimization of the approximate integration of set-valued functions from the class specified by a given majorant of their moduli of continuity performed by using the values of these functions at n fixed or free points of their domain.

Brief Communications (Russian)

Optimization of interval formulas for approximate integration of set-valued functions monotone with respect to inclusion

Babenko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 11. - pp. 1565-1569

The best interval quadrature formula is obtained for the class of convex set-valued functions defined on the segment [0, 1] and monotone with respect to inclusion.

Article (Russian)

Optimization of approximate integration of set-valued functions monotone with respect to inclusion

Babenko V. F., Babenko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 147-155

The best quadrature formula is found for the class of convex-valued functions defined on the interval [0, 1] and monotone with respect to an inclusion.