Could I find the inverse function of the following integral equation?
I am going to write it as $h(x)=...$
The integral equation is:
$$R(i) = \int_{y\in S} {\frac{{w(y) g(y,i)_{}^\sigma }}{{\int_{x\in S} {h(x)g(x,y)_{}^\sigma f(x,y)_{}^\sigma dx} }}dy} $$ where S is a compact subset of a two-dimensional surface which has positive Lebesgue measure. $w(y)$ and $h(x)$ are weights, $w(y):S\rightarrow (0,1)$ and $h(x):S\rightarrow (0,1)$. $g(x,y)$ is a function which measure the distance between points x and y,$g(x,y):S \times S \rightarrow \mathbb{R}_+$, $g(y,x)=g(x,y)$. f(x,y) =a(x)/a(y),where a(x) is treat as a random variable which draws independently from Frechet distribution . $\sigma $ is a constant.