Suppose $f\in C([0,\frac{3}{4}]^2)$ and
$$\begin{array}{rlr}\text{i.}& \int_0^{\frac{3}{4}-x} f(x,y)dy=-\frac{1}{2}x^2+\frac{9}{32}&\forall x\in [0,\frac{3}{4}]\\ \text{ii.}& \int_0^{\frac{3}{4}-y} f(x,y)dx= \frac{1}{2}y^2-y+\frac{15}{32}&\forall y\in [0,\frac{3}{4}]\\ \text{iii.}& 0\leq f(x,y)\leq 1\end{array}$$
Does the system of equations (i)-(iii) has a solution and how could I recover the kernel $f$?.
Thanks.