Q:

A subadditive functional which is not a convex functional

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

A:

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.

