Robert Hakl, Sulkhan Mukhigulashvili

On One Estimate for Periodic Functions

Abstract:
For $v \in \widetilde{C}_{\omega}^{n}$ $(n \in N$, $\omega >0)$, the estimate
$$ \triangle\left( v\right) < \frac{\omega^{n}}{d_{n}}\triangle\left(v^{(n)}\right) $$
is derived, where
$$ \triangle\left(v^{(i)}\right)=\max \left\{v^{(i)}(t):t\in R \right\}-\min \left\{ v^{(i)}(t):t\in R \right\} \quad (i=\overline {0,n})$$
and $d_n$ are defined by a certain recurrent formula.

Keywords:
Periodic functions, inequalities involving derivatives.

MSC 2000: 26D10