2018
Том 70
№ 4

All Issues

Shumeiko A. A.

Articles: 7
Anniversaries (Ukrainian)

Motornyi Vitalii Pavlovych (on his 75th birthday)

Babenko V. F., Davydov O. V., Kofanov V. A., Parfinovych N. V., Pas'ko A. N., Romanyuk A. S., Ruban V. I., Samoilenko A. M., Shevchuk I. A., Shumeiko A. A., Timan M. P., Trigub R. M., Vakarchuk S. B., Velikin V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 995-999

Article (Russian)

On Jackson-Type Inequalities for Functions Defined on a Sphere

Babenko V. F., Doronin V. G., Ligun A. A., Shumeiko A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 291–304

We obtain exact estimates of the approximation in the metrics $C$ and $L_2$ of functions, that are defined on a sphere, by means of linear methods of summation of the Fourier series in spherical harmonics in the case where differential and difference properties of functions are defined in the space $L_2$.

Article (Russian)

Recovery of a Function from Information on Its Values at the Nodes of a Triangular Grid Based on Data Completion

Ligun A. A., Shumeiko A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 332-341

We consider a method for binary completion of two-dimensional data. On the basis of information about a surface given by a triangular grid, we construct a continuous polygonal surface based on a denser grid (than the one given). We determine the error and norm of this method and study its properties.

Article (Ukrainian)

A Linear Method for the Recovery of Functions Based on Binary Data Completion

Ligun A. A., Shumeiko A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 11. - pp. 1501-1512

We construct a linear recovery method based on binary data completion using the Bessel interpolation formula. We find an asymptotic value of the error of this method, determine its norm, and study its properties.

Article (Russian)

On asymptotically optimal weight quadrature formulas on classes of differentiable functions

Ligun A. A., Shumeiko A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 2. - pp. 234-248

We investigate the problem of asymptotically optimal quadrature formulas with continuous weight function on classes of differentiable functions.

Article (Russian)

On lower bounds for the approximation of functions by local splines with nonfixed nodes

Shumeiko A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 1. - pp. 134-144

For functions integrable to the power \(\beta = (r + 1 + 1/p)^{ - 1} \) , we obtain asymptotically exact lower bounds for the approximation by local splines of degree r and defect k< r/2 in the metric of L p

Article (Russian)

On one problem of minimization of area

Ligun A. A., Shumeiko A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 927–936

We consider the problem of asymptotically optimal location of disks with equal radii for the minimization of the are of the figure bounded by a given curve and a connected union of these disks.