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