On the best approximation of the Hölder classes by linear methods

TitleOn the best approximation of the Hölder classes by linear methods
Publication TypeJournal Article
Year of Publication2014
AuthorsSkorokhodov, DS
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.08.041
Issue8
SectionMathematics
Pagination41-47
Date Published8/2014
LanguageRussian
Abstract

We find exact values of linear one-dimensional widths of the Hölder classes in the space C. The error of the best approximation of the Hölder classes by a wide class of linear positive methods is determined.

Keywordsbest approximation, Hölder classes, linear methods
References: 

1. Korneychyk N. P. Extremal problems of approximation theory, Moscow: Nauka, 1976 (in Russian).
2. Tikhomirov V. M. Some problems in approximation theory, Moscow: Izd-vo Mosk. un-ta, 1976 (in Russian).
3. Korneychyk N. P. Splines in approximation theory, Moscow: Nauka, 1984 (in Russian).
4. Korneychyk N. P. Exact constants in approximation theory, Moscow: Nauka, 1987 (in Russian).
5. Grigoryan Yu. I. Mat. zametki, 1973, 13, No 5: 637–646 (in Russian).
6. Korneychyk N. P. Dop. AN UkrSSR, 1963, 150, No 6: 1218–1220 (in Russian).
7. Korneychyk N. P. Izv. AN USSR. Ser. matem., 1971, 35, No 1: 93–124 (in Russian).
8. Ruban V. I. Mat. zametki, 1974, 15, No 3: 387–392 (in Russian).
9. Korneychyk N. P. Ukr. mat. zhurn., 1996, 48, No 9: 1255–1264 (in Russian).
10. Korneychyk N. P. Uspekhi mat. nauk, 1974, 29, No 3(177): 9–42 (in Russian).
11. Zorich V. A. Mathematical analysis. Pt. II, Moscow: MTsNMO, 2002 (in Russian).
12. Krasnoselskiy M. A., Lifshyts E. A., Sobolev A. V. Positive linear systems: the method of positive operators, Moscow: Nauka, 1985 (in Russian).