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I would like to solve this problem, but I do not know how ...

Let $f:(0;1) \rightarrow \mathbb{R}$ be a function such that: $$\lim_{x \to0^+}f(x)=0$$ and such that there exists $0<\lambda<1$ such that: $$\lim_{x \to0^+} \frac{ \left [ f(x)-f(\lambda x) \right ]}{x}=0$$ prove that $$\lim_{x \to0^+} \frac{f(x)}{x}=0$$

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You might be able to use math.stackexchange.com/questions/89575/… Martin Sleziak's answer in particular. –  David Mitra Jan 10 '12 at 0:05
    
tanks!!!!!!!!!! –  FrConnection Jan 10 '12 at 0:15

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