4
$\begingroup$

Let $f$ be a function from $\mathbb{R}^n$ to $\mathbb{R}$, which is convex & concave and continuous with $f(0)=0$. How to prove that $f(x)=q\cdot x$ for all $x$ in $\mathbb{R}^n$, for a scalar $q$?

I have shown $f(wx)=wf(x)$ for $w$ in $[0,1]$.

  • 3
    $q$ is not a scalar but a vector (we take the inner product with $x$).2012-04-10

1 Answers 1