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I have a question

$$\Psi: z\in\mathbb{R}\rightarrow\mathbb{R}_+$$

with $\Psi(0)=1$.

Could someone give a simple class of the function $\Psi$ such that the following inequality holds:

$$c|\Psi'(z)|\leq |1-z\frac{\Psi'(z)}{\Psi(z)}|,\ \ \forall z\in\mathbb{R}$$

Many thanks

1 Answers 1