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.
Convex functions
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analysis
convex-analysis
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2Did you try differentiating twice? – 2011-08-13
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0Writing 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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0Thanks guys, I have managed to solve it now :) – 2011-08-14
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2Could you add your proof? – 2012-04-05