О неравенствах для норм промежуточных производных на конечном интервале
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 ‖‖f(n−2)‖‖∞⩽4n−2(n−1)!‖f‖∞+‖‖f(n)‖‖∞/2 holds with the exact constant 4 n−2(n−1)!.
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| Date: | 1995 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Інститут математики НАН України
1995
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| Series: | Український математичний журнал |
| Subjects: | |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | О неравенствах для норм промежуточных производных на конечном интервале / В.Ф. Бабенко, С.А. Кофанов, С.А. Пичугов // Український математичний журнал. — 1995. — Т. 47, № 1. — С. 105–107. — Бібліогр.: 4 назв. — рос. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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
‖‖f(n−2)‖‖∞⩽4n−2(n−1)!‖f‖∞+‖‖f(n)‖‖∞/2
holds with the exact constant 4 n−2(n−1)!. |
|---|