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How does one show that $\phi(x)$ convex and twice differentiable implies that $x\phi(\frac{y}{x})$ is convex on the plane $x>0$? Thanks.

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    Did you try differentiating twice?2011-08-13
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    Writing phi as a supremum of affine functions yields a simple proof which explains why the restriction to x>0 is needed (and why the hypothesis that phi is twice differentiable is not).2011-08-13
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    Thanks guys, I have managed to solve it now :)2011-08-14
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    Could you add your proof?2012-04-05

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