Probably a very basic question: Let's assume that we have a $L$-Lipschitz ($L>0$) function $f(x)$. Can we say the following?: $$ L\text{- Lipschitz } (L>0) \text{ function } f(x) \iff f(x) \text{ is monotonically increasing } $$
2026-03-26 07:58:33.1774511913
$L\text{- Lipschitz } (L>0) \text{ function } f(x) \iff f(x) \text{ is monotonically increasing }$?
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$\sqrt[3]{x}$ is monotonically increasing but not Lipschitz continuous. $\sin x$ is Lipschitz continuous but not monotone.