# A subadditive functional which is not a convex functional

• If $T$ is a subadditive functional which is homogeneous of order $1$, then it is convex. – saz Jan 10 at 12:27
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.