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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

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$\{\Psi:z\mapsto 1\}$. Why are you asking?

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    Thank you for your reply. I would like to know whether we can try to give a general class of such functions. We hope this function can be writen in a closed form with some parameters to chose: $$\Psi=\Psi(z,\alpha),\ \ \alpha\in A$$ where $A$ is a set such that the previous inequality holds.2012-08-20
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    How can you hope with only a vague bound on the derivative to be able to _parametrize_ these functions?? There must be _way_ too many of them for that.2012-08-21