Let's have the following function $f:\mathbb{R}^{2}\to\mathbb{R}$ defined by $|x+y|$, is it convex?
We have $\lambda\in (0,1),x,y\in$ dom$(f)$, so $|\lambda x+(1-\lambda)y|\le \lambda |x| + (1-\lambda)|y|$. It means the function is convex according to the definition of a convex function. Is it correct?