Abstract:
The following result is proved in the paper: if for some real $A>0$ and some natural number $n>1$
for all $x$ from $[0,1]$ we have the inequality $|f^{(n)}(x)|\geq A,$ then the following estimate is valid:
$$
|I|=\left|\int_0^1\limits\rho(f(x))~dx\right|\leq\min{\{1;4nA^{-1/n}\}},
$$
where $\rho(t)=0,5-\{t\}.$
Fulltext:
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