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On inequalities for norms of intermediate derivatives on a finite interval

Authors:

V F Babenko V A Kofanov S A Pichugov

Institution:

1. Dnepropetrovsk University, Dnepropetrovsk

Abstract:

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

$\left\\| {f^{(n - 2)} } \right\\|_\infty \leqslant 4^{n - 2} (n - 1) ! \left\\| f \right\\|_\infty + \left\\| {f^{(n)} } \right\\|_\infty /2$

Keywords:
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