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August 23rd, 2017, 02:33 AM   #1
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Jensen +

Hi,

$\displaystyle \textbf{ Jensen + : } g \in C^2([0,1]) \text{ with }f\in C^1([0,1],[0,1]) \text{ and }f(0)=f(1)=0.
\\\text{Is it true that : }|g(\int_0^1 f(x)\text{d}x) -\int_0^1g(f(x))\text{d}x | \leq \frac{1}{10}\max(|g''|)|\times \max(|f'|)^2 ?$

Cordially.
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