# name for a class of functions

I would like to ask whether is used some name for functions $g:A\to\mathbb{R}$, $A\subset \mathbb{R}$, for which $$\exists \lambda>1:\;\; \lim_{x\to 0^+}\frac{\lambda g(x)}{g(\lambda x)}>1.$$

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What is A ? And RA ? – David Roberts Dec 1 '12 at 11:43
Let just $A=[0,1]$ – user27381 Dec 1 '12 at 15:52