Shortlist ONM 2010 ,pb25

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Laurentiu Tucaa
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Shortlist ONM 2010 ,pb25

Post by Laurentiu Tucaa »

Fie \( p>0 \) si \( f:[0,1]\rightarrow\mathbb{R} \) continua ,concava a.i. \( f(0)=1 \).Aratati ca \( (p+1)\int_0^1 x^{2p}f(x)dx+\frac{2p-1}{8p+4}\le(\int_0^1 f(x)dx)^2 \) si aflati cazurile de egalitate.
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