August 23rd, 2017, 02:33 AM  #1 
Member Joined: May 2017 From: France Posts: 57 Thanks: 1  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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