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I have been thinking about this for a while now, is there a subadditive functional which is not a convex functional?

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  • $\begingroup$ If $T$ is a subadditive functional which is homogeneous of order $1$, then it is convex. $\endgroup$ – saz Jan 10 at 12:27
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On the real line $|\sin (x+y)| =|\sin\, x \cos\, y+\cos\, x \sin \,y| \leq |\sin (x)|+|\sin (y)|$ but $|\sin (x)|$ is not convex.

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  • $\begingroup$ Sir, you're real good! (+1) $\endgroup$ – Omojola Micheal Jan 10 at 12:57

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