What is the proof for the statement $a^c + b^c > (a + b)^c$ when $0 < c < 1$, $a, b> 0$ and $1/c$ is non-integral? I have a very simple proof for this statement when $1/c$ is an integer (namely, just raise both sides to $1/c$ and the proof immediately follows from binomial expansion of $(a^c + b^c)^{1/c}$).

But what about the case when $1/c$ is non-integral?