2019
Том 71
№ 9

All Issues

Hnatyuk Yu. V.

Articles: 5
Article (Ukrainian)

Relative Chebyshev point of a system of continuously varying bounded closed sets

Hnatyuk Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 889-903

For the problem of finding a relative Chebyshev point of a system of continuously varying (in the sense of the Hausdorff metric) bounded closed sets of a normed space linear over the field of complex numbers, we establish some existence and uniqueness theorems, necessary and sufficient conditions, and criteria for a relative Chebyshev point and describe properties of the extremal functional and the extremal operator.

Article (Ukrainian)

The best uniform approximation in the metric space of continuous maps with compact convex images

Hnatyuk Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 12. - pp. 1620 - 1633

For the problem of the best uniform approximation of a continuous map with compact convex images by sets of other continuous maps with compact convex images, we establish necessary and sufficient conditions and the criterion for an extremal element, which is a generalization of the classical Kolmogorov criterion for the polynomial of best approximation.

Article (Ukrainian)

Algorithms for the Best Simultaneous Uniform Approximation of a Family of Functions Continuous on a Compact Set by a Chebyshev Subspace

Hnatyuk Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 3. - pp. 291-306

We generalize the cutting-plane method and the Remez method to the case of the problem of the best simultaneous uniform approximation of a family of functions continuous on a compact set.

Brief Communications (Ukrainian)

Best Uniform Approximation of a Family of Functions Continuous on a Compact Set

Hnatyuk Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1574-1580

We investigate the problem of the best uniform approximation of a function continuous on a compact set. We generalize the principal results of this investigation to the problem of the best simultaneous uniform approximation of a family of functions continuous on a compact set.

Article (Ukrainian)

Basic properties of the problem of the best simultaneous approximation of several elements

Hnatyuk Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 9. - pp. 1183–1193

For the problem of the best approximation of several elements with respect to the maximum of convex-concave fractional functions with additional restrictions, we establish duality relations and criteria for the element of the best approximation.