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