On exact constants in inequalities for norms of derivatives on a finite segment
We prove that, in an additive inequality for norms of intermediate derivatives of functions defined on a finite segment and equal to zero at a given system of points, the least possible value of a constant coefficient of the norm of a function coincides with the exact constant in the corresponding M...
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| Date: | 1999 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4588 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510735143010304 |
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| author | Babenko, V. F. Uedraogo, Zh. B. Бабенко, В. Ф. Удраого, Ж. Б. Бабенко, В. Ф. Удраого, Ж. Б. |
| author_facet | Babenko, V. F. Uedraogo, Zh. B. Бабенко, В. Ф. Удраого, Ж. Б. Бабенко, В. Ф. Удраого, Ж. Б. |
| author_sort | Babenko, V. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:09:14Z |
| description | We prove that, in an additive inequality for norms of intermediate derivatives of functions defined on a finite segment and equal to zero at a given system of points, the least possible value of a constant coefficient of the norm of a function coincides with the exact constant in the corresponding Markov-Nikol'skii inequality for algebraic polynomials that are also equal to zero at this system of points. |
| first_indexed | 2026-03-24T03:01:43Z |
| format | Article |
| fulltext |
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We prove that, in the additive inequality for norms of intermediate derivatives of functions which are
defined on a finite interval and are equal to zero in a given system of points, the least possible value of a
constant with the norm of function coincides with an exact constant in the corresponding Markov-
Nikol'skii inequality for algebraic polynomials which are also equal to zero in this system of points.
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C. 25-27; 113-117.
Ho.qy~lCHO 21.08.96
ISSN 0041-6053. YKp. ~wan. ~.'~pn., 1999, m. 51,1~ 1
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| id | umjimathkievua-article-4588 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:01:43Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/91/4a531f35899a30b5e72fccb186106691.pdf |
| spelling | umjimathkievua-article-45882020-03-18T21:09:14Z On exact constants in inequalities for norms of derivatives on a finite segment О точных константах в неравенствах для норм производных на конечном отрезке Babenko, V. F. Uedraogo, Zh. B. Бабенко, В. Ф. Удраого, Ж. Б. Бабенко, В. Ф. Удраого, Ж. Б. We prove that, in an additive inequality for norms of intermediate derivatives of functions defined on a finite segment and equal to zero at a given system of points, the least possible value of a constant coefficient of the norm of a function coincides with the exact constant in the corresponding Markov-Nikol'skii inequality for algebraic polynomials that are also equal to zero at this system of points. Доведено, що в адитивній нерівності для норм проміжних похідних функцій, які визначені на скінченному відрізку і дорівнюють нулю у заданій системі точок, найменше можливе значення константи при нормі функції співпадає з точною константою у відповідній нерівності типу Маркова - Нікольського для алгебраїчних поліномів, які теж дорівнюють нулю у цій системі точок. Institute of Mathematics, NAS of Ukraine 1999-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4588 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 1 (1999); 117–119 Український математичний журнал; Том 51 № 1 (1999); 117–119 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4588/5880 https://umj.imath.kiev.ua/index.php/umj/article/view/4588/5881 Copyright (c) 1999 Babenko V. F.; Uedraogo Zh. B. |
| spellingShingle | Babenko, V. F. Uedraogo, Zh. B. Бабенко, В. Ф. Удраого, Ж. Б. Бабенко, В. Ф. Удраого, Ж. Б. On exact constants in inequalities for norms of derivatives on a finite segment |
| title | On exact constants in inequalities for norms of derivatives on a finite segment |
| title_alt | О точных константах в неравенствах для норм производных на конечном отрезке |
| title_full | On exact constants in inequalities for norms of derivatives on a finite segment |
| title_fullStr | On exact constants in inequalities for norms of derivatives on a finite segment |
| title_full_unstemmed | On exact constants in inequalities for norms of derivatives on a finite segment |
| title_short | On exact constants in inequalities for norms of derivatives on a finite segment |
| title_sort | on exact constants in inequalities for norms of derivatives on a finite segment |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4588 |
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