I am looking for a reference/proof under which conditions the following Volterra integral equation of the first kind has a unique solution:
$$H(x)=\int_0^xK(x,y)g(y)dy$$
with $x\in[0,1]$, $y\in [0,1]$ and $H(x)$ is a (weakly) increasing function and $K(x,y)$ is increasing in $x$. I guess that this is a contraction mapping and so a solution always exists, but for uniqueness I am not sure how to proceed further...
Could one say anything at this level of generality?