The Exact Inequalities of Jackson–Stechkin Type and the Width Values for Some Classes of Functions in L₂ Space
In this paper, some exact inequalities between the best approximations of periodic differentiable functions with trigonometric polynomials and generalized moduli of the continuity Ωm of m-th order in L₂[0, 2π] space are found. Similar averaged characteristics of function smoothness in studying the i...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-10-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/176 |
| _version_ | 1797877894098190336 |
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| author | M. R. Langarshoev |
| author_facet | M. R. Langarshoev |
| author_sort | M. R. Langarshoev |
| collection | DOAJ |
| description | In this paper, some exact inequalities between the best approximations of periodic differentiable functions with trigonometric polynomials and generalized moduli of the continuity Ωm of m-th order in L₂[0, 2π] space are found. Similar averaged characteristics of function smoothness in studying the important problems in the constructive theory of functions were considered by K.V. Runovskiy, E.A. Strogenko, V.G. Krotov, P. Osvald and many others. For some classes of functions defined by indicated moduli of continuity where the r-th derivatives are bounded by functions which satisfy certain constraints were obtained the exact values of Bernstein, Gelfand, Kolmogorov, linear and projection n-widths. Here is given an example of a majorant for which all the stated claims are fulfilled. |
| first_indexed | 2024-04-10T02:25:13Z |
| format | Article |
| id | doaj.art-ada9fe3676c043a7a90c1ff4d8edd86f |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:25:13Z |
| publishDate | 2013-10-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-ada9fe3676c043a7a90c1ff4d8edd86f2023-03-13T08:07:32ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-10-012059010510.18255/1818-1015-2013-5-90-105170The Exact Inequalities of Jackson–Stechkin Type and the Width Values for Some Classes of Functions in L₂ SpaceM. R. Langarshoev0Таджикский национальный университетIn this paper, some exact inequalities between the best approximations of periodic differentiable functions with trigonometric polynomials and generalized moduli of the continuity Ωm of m-th order in L₂[0, 2π] space are found. Similar averaged characteristics of function smoothness in studying the important problems in the constructive theory of functions were considered by K.V. Runovskiy, E.A. Strogenko, V.G. Krotov, P. Osvald and many others. For some classes of functions defined by indicated moduli of continuity where the r-th derivatives are bounded by functions which satisfy certain constraints were obtained the exact values of Bernstein, Gelfand, Kolmogorov, linear and projection n-widths. Here is given an example of a majorant for which all the stated claims are fulfilled.https://www.mais-journal.ru/jour/article/view/176наилучшее приближениеобобщенный модуль непрерывностиэкстремальная характеристикаn-поперечники |
| spellingShingle | M. R. Langarshoev The Exact Inequalities of Jackson–Stechkin Type and the Width Values for Some Classes of Functions in L₂ Space Моделирование и анализ информационных систем наилучшее приближение обобщенный модуль непрерывности экстремальная характеристика n-поперечники |
| title | The Exact Inequalities of Jackson–Stechkin Type and the Width Values for Some Classes of Functions in L₂ Space |
| title_full | The Exact Inequalities of Jackson–Stechkin Type and the Width Values for Some Classes of Functions in L₂ Space |
| title_fullStr | The Exact Inequalities of Jackson–Stechkin Type and the Width Values for Some Classes of Functions in L₂ Space |
| title_full_unstemmed | The Exact Inequalities of Jackson–Stechkin Type and the Width Values for Some Classes of Functions in L₂ Space |
| title_short | The Exact Inequalities of Jackson–Stechkin Type and the Width Values for Some Classes of Functions in L₂ Space |
| title_sort | exact inequalities of jackson stechkin type and the width values for some classes of functions in l₂ space |
| topic | наилучшее приближение обобщенный модуль непрерывности экстремальная характеристика n-поперечники |
| url | https://www.mais-journal.ru/jour/article/view/176 |
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