On inequalities for norms of intermediate derivatives on a finite interval
For functionsf which have an absolute continuous (n−1)th derivative on the interval [0, 1], it is proved that, in the case ofn>4, the inequality $$\left\| {f^{(n - 2)} } \right\|_\infty \leqslant 4^{n - 2} (n - 1) ! \left\| f \right\|_\infty + \left\| {f^{(n)} } \right\|_\infty /2$$ holds...
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| Datum: | 1995 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1995
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5387 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511618426732544 |
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| author | Babenko, V. F. Kofanov, V. A. Pichugov, S. A. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. |
| author_facet | Babenko, V. F. Kofanov, V. A. Pichugov, S. A. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. |
| author_sort | Babenko, V. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T08:58:17Z |
| description | For functionsf which have an absolute continuous (n−1)th derivative on the interval [0, 1], it is proved that, in the case ofn>4, the inequality $$\left\| {f^{(n - 2)} } \right\|_\infty \leqslant 4^{n - 2} (n - 1) ! \left\| f \right\|_\infty + \left\| {f^{(n)} } \right\|_\infty /2$$ holds with the exact constant 4 n−2(n−1)!. |
| first_indexed | 2026-03-24T03:15:45Z |
| format | Article |
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| id | umjimathkievua-article-5387 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:15:45Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/6d/69d395c7c7d17b72c52474a541aae86d.pdf |
| spelling | umjimathkievua-article-53872020-03-19T08:58:17Z On inequalities for norms of intermediate derivatives on a finite interval О неравенствах для норм промежуточных производных на конечном интервале Babenko, V. F. Kofanov, V. A. Pichugov, S. A. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. For functionsf which have an absolute continuous (n−1)th derivative on the interval [0, 1], it is proved that, in the case ofn>4, the inequality $$\left\| {f^{(n - 2)} } \right\|_\infty \leqslant 4^{n - 2} (n - 1) ! \left\| f \right\|_\infty + \left\| {f^{(n)} } \right\|_\infty /2$$ holds with the exact constant 4 n−2(n−1)!. Доведено, що при $n > 4$ для функцій $f$, які мають на $[0, 1]$ абсолютно неперервну похідну порядку $n - 1$, викопується нерівність $$\left\| {f^{(n - 2)} } \right\|_\infty \leqslant 4^{n - 2} (n - 1) ! \left\| f \right\|_\infty + \left\| {f^{(n)} } \right\|_\infty /2$$ з точною константою $4^{n-2}(n - 1)!$. Institute of Mathematics, NAS of Ukraine 1995-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5387 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 1 (1995); 105–107 Український математичний журнал; Том 47 № 1 (1995); 105–107 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5387/7465 https://umj.imath.kiev.ua/index.php/umj/article/view/5387/7466 Copyright (c) 1995 Babenko V. F.; Kofanov V. A.; Pichugov S. A. |
| spellingShingle | Babenko, V. F. Kofanov, V. A. Pichugov, S. A. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. On inequalities for norms of intermediate derivatives on a finite interval |
| title | On inequalities for norms of intermediate derivatives on a finite interval |
| title_alt | О неравенствах для норм промежуточных производных на конечном интервале |
| title_full | On inequalities for norms of intermediate derivatives on a finite interval |
| title_fullStr | On inequalities for norms of intermediate derivatives on a finite interval |
| title_full_unstemmed | On inequalities for norms of intermediate derivatives on a finite interval |
| title_short | On inequalities for norms of intermediate derivatives on a finite interval |
| title_sort | on inequalities for norms of intermediate derivatives on a finite interval |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5387 |
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