As we know, general solution of the linear functional equation $f(x+1)-f(x)=g(x)$ ($g$ is a known function) is $f=f_0+\phi$, where $f_0$ is an its special solution and $\phi$ any 1-periodic function.

Now, does any one know **general solution** of the linear functional equation: $$rf(ax+b)+sf(cx+d)=g(x),$$ where $a,b,c,d, r$ and $s$ are real constants with $rasc\neq0$?

($g$ is a given real function, the case $g=0$ and the equation $f(ax+b)=cf(x)$ is of special interest).

Are there any papers or books regarding the problem?