On the Landau-Kolmogorov inequality between $\| f' \|_{\infty}$, $\| f \|_{\infty}$ and $\| f''' \|_1$
Copyright policy )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 linear bounded ones and the best recovery of operator $D^1$ on elements of a class given with error.
best recovery of operator, QA1-939, Approximation by operators (in particular, by integral operators), Landau-Kolmogorov problem, Inequalities involving derivatives and differential and integral operators, Stechkin problem, Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), the Landau-Kolmogorov problem, Mathematics, the Stechkin problem, modulus of continuity of operator
best recovery of operator, QA1-939, Approximation by operators (in particular, by integral operators), Landau-Kolmogorov problem, Inequalities involving derivatives and differential and integral operators, Stechkin problem, Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), the Landau-Kolmogorov problem, Mathematics, the Stechkin problem, modulus of continuity of operator
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