Some linear integral equation

Question

Please help me with the following problem: Let $\gamma\in (0,1)$ and $a<0<b$, $-a<b$, and $x\geq0$. Solve the following equation $$f(x)=\frac{\gamma}{b-a}\int_{\max(a+x,0)}^{b+x}f(y)dy$$ I try to solve this using Banach contraction theorem. Unfortunately if I put $f_0=1$ I get $f_1$ with two different expression over intervals $[0,-a]$ and $[-a,\infty)$. Then $f_2$ will be define over three intervals $[0,-a], [-a,-2a],[-2a,\infty)$ Besides that one can see that the degree of the polynomials will be increasing in some intervals. Do you have any idea how can I force with this?