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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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    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