Given the following conditions;
\begin{align} f[y_1(x)]f[y_2(x)] - \left\lbrace 1 - f[y_2(x)] \right\rbrace \omega(x) &= 0\\ f(0) &= 0\\ f(\infty) &= 1, \end{align} I'd like to find function $f$, which is continuous. The functions $y_1$, $y_2$ and $\omega$ are all known and continuous. $y_1$ and $y_2$ are also strictly monotonic.
Is there an approach to compute the function $f$ numerically?
Thank you.