If $f\in C^1(\mathbb R)$ satisfies $f'(x)>f(f(x))$ for all $x\in\mathbb R$, then $f(f(f(x)))\leq0$ for all $x\geq0$.
Could anybody provide a solution or some hints on this problem?
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Keke Zhang
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. – José Carlos Santos Dec 19 '17 at 14:50
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The context of this problem could help. – ajotatxe Dec 19 '17 at 14:59