# Comp Complex Variables – Simplifying a Complex General Function

Consider the following complex function:

$$frac {1} {1+ lambda f (z) f ( frac {1} {z})},$$

or $$lambda$$ is a real constant number and $$z$$ is a complex variable.
I need to find a function $$G (z)$$ such as

$$G (z) times G ( frac {1} {z}) = frac {1} {1+ lambda f (z) f ( frac {1} {z})}.$$

Can we find $$G (z)$$ as a function of $$f$$?

Can we solve the problem if $$f$$ is a polynomial function?