Let $f: [0,1]^2 \to R$ be an arbitrary continuous in both arguments and increasing in the first argument function, and let $h: [0,1]^2 \to [0,1]$ be some arbitrary function.
Does $\forall f,h$ there exists $g: R^2 \to R$ such that $\int_0^1f(x,h(z,y))dy=f(x,g(x,z))$ $\forall x,z$?
Thank you!!!