Babenko V. V.
Approximation of some classes of set-valued periodic functions by generalized trigonometric polynomials
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.
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.
Optimization of interval formulas for approximate integration of set-valued functions monotone with respect to inclusion
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.
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.
Optimization of quadratures on classes of functions given by differential operators with Real Spectra
Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 291-300
We study the problem of optimization of quadrature formulas for broad classes of periodic functions defined in terms of differential operators with real spectra. We analyze quadrature formulas containing values of functions and values of the images of functions under the action of some differential operators. The rectangular formula is proved to be optimal.