On the Landau-Kolmogorov inequality between $$$\| f' \|_{\infty}$$$, $$$\| f \|_{\infty}$$$ and $$$\| f''' \|_1$$$

D. Skorokhodov

doi:10.15421/241906

On the Landau-Kolmogorov inequality between $$$\| f' \|_{\infty}$$$, $$$\| f \|_{\infty}$$$ and $$$\| f''' \|_1$$$

D. Skorokhodov (Oles Honchar Dnipro National University), https://orcid.org/0000-0001-8494-5885

Abstract

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.

Keywords

the Landau-Kolmogorov problem; the Stechkin problem; best recovery of operator; modulus of continuity of operator

MSC 2020

41A17; 41A35; 26D10

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