Functie convexa de ordinul 3

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opincariumihai
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Functie convexa de ordinul 3

Post by opincariumihai »

Aratati ca o functie convexa de ordinul 3 este derivabila si derivata este convexa. (T. Popoviciu )

\( f:I\rightarrow R,\ I \) interval nedegenerat, se numeste convexa de ordinul n daca \( \forall x_0,x_1,...,x_n\in{I} \) distincte, avem ca \( [x_0,x_1,...x_{n+1}; f] \geq 0 \) unde \( [x_0,x_1,...x_{n+1}; f]= \sum_{i=0}^{n+1} \frac{f(x_i)}{ \omega ^,(x_i)} \) cu \( \omega(x)=(x-x_0)...(x-x_{n+1}) \)
Last edited by opincariumihai on Sat Oct 03, 2009 10:55 pm, edited 5 times in total.
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