On the Landau-Kolmogorov inequality between $\| f' \|_{\infty}$, $\| f \|_{\infty}$ and $\| f''' \|_1$
We solve the Landau-Kolmogorov problem on finding sharp additive inequalities that estimate $\| f' \|_{\infty}$ in terms of $\| f \|_{\infty}$ and $\| f''' \|_1$. Simultaneously we solve related problems of the best approximation of first order differentiation operator $D^1$ by l...
| Published in: | Researches in Mathematics |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Oles Honchar Dnipro National University
2019-07-01
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| Subjects: | |
| Online Access: | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/113 |
| Summary: | We solve the Landau-Kolmogorov problem on finding sharp additive inequalities that estimate $\| f' \|_{\infty}$ in terms of $\| f \|_{\infty}$ and $\| f''' \|_1$. Simultaneously we solve related problems of the best approximation of first order differentiation operator $D^1$ by linear bounded ones and the best recovery of operator $D^1$ on elements of a class given with error. |
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| ISSN: | 2664-4991 2664-5009 |