I have been playing around with recursive definition of functions. I posed myself this question. Suppose functions $g,h$ are given $\mathbb R \to \mathbb R$ functions, and
$$f(x) = g(x) + h(f(x))$$
Can I construct the function $f(x)$ from this definition? What are the requirements on $g,h$ so that $f$ exists?
My idea was that I can write perhaps
$$f(x) = g(x) + h(g(x) + h(g(x) + h(\dots)))$$
and depending on $g,h$ this might converge somehow so that $f(x)$ on the rhs becomes negligible. But I don't know how I can perform the convergence.