# Shumeiko A. A.

### 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.

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

### On Jackson-Type Inequalities for Functions Defined on a Sphere

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

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 $L_2$.

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

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.

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

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.

### Description of Convex Curves

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 908-922

We present a description of convex curves, which enables one to reduce the problem of approximation of a convex curve by piecewise circular lines in the Hausdorff metric to the problem of approximation of 2π-periodic functions by trigonometric splines in the uniform metric. We describe certain properties of convex curves.

### On approximation of functions from below by splines of the best approximation with free nodes

Ukr. Mat. Zh. - 2000. - 52, № 4. - pp. 512-523

Let M be the set of functions integrable to the power β=(*r*+1+1/*p*)^{-1}. We obtain asymptotically exact lower bounds for the approximation of individual functions from the set M by splines of the best approximation of degree *r*and defect *k* in the metric of *L* _{p}.

### On asymptotically optimal weight quadrature formulas on classes of differentiable functions

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.

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

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 }

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

Ukr. Mat. Zh. - 1999. - 51, № 12. - pp. 1628–1637

For functions with the integrable βth power, where β = (*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}.

### On a problem of restoration of curves

Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 181–189

We investigate the problem of asymptotically optimal placement of disks of the same radius under the condition of minimization of the Hausdorff distance between a given curve $Γ$ and the union of disks under study.

### On one problem of minimization of area

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.