If $f(x)$ is a non decreasing concave function between $0$ and $1$ for $x\ge 0$, then for $a>1$ I am confident that $af(x)>f(ax)$, but I am not quite sure how to prove it. Any help would be appreciated.
2026-04-03 11:51:39.1775217099
Proof for special concave form of functions
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I actually found the proof. It actually applies to concave functions greater than zero. If there is interest I can post the proof.