Hey guys, can any of you tell me if there's a function (f(x): R->R) apart from linear, that satisfies the following:

f( (x - f(x))/2 ) = C * f(x)

where C is a real constant. I don't really know how to touch this problem... I'm a physics PhD student interested in fractal-like behaviour, and the answer to this question would help me a great deal. Even if it turns out, that no such function exists.

Thanks a lot for your help!