I was wondering if there were methods to solve a system of coupled integral equations. The example case I am thinking about is
$$f(x)=g(x)+\int_a^xf(x^\prime)h(x^\prime) dx^\prime$$
$$h(x)=k(x)+\int_b^x l(x^\prime)h(x^\prime) dx^\prime $$
where g, k, and l are known functions and h and f are unknown. Any suggestions on where to look, or alternative methods for this type of system would be great!