Hello, I am trying to solve the functional equation below. Can anybody help? I don't expect a solution, but tips on how to do it, tricks or references to usefull books.

Thank you
Jan

The notation is following. Let \pi>0,~\phi>0,~\delta<br /> \in(0,1),~p\in(0,1), all of them parameters of the problem. Then
the problem is to find real-valued function
q_{d}(x):\mathbb{R}\rightarrow\mathbb{R} which satisfies
\frac{[q_{d}(x)-\pi-\phi\delta<br /> p](1-p)}{\sqrt{D_{1}}}+\frac{[q_{d}(x)-\pi-\phi(1-\delta(1-p))]p}{\sqrt{D_{2}}}-\frac{q_{d}(x)-\pi-\phi<br /> p}{\sqrt{D_{3}}}=0<br />
where
D_{1}=\frac{1}{1-\delta}[[q^{-1}_{d}(q_{a}(q_{d}(x)))-\pi-\phi(1-\delta(1-p))]^{2}-\delta[q_{a}(q_{d}(x))-\pi-\phi<br /> p]^{2}]\\+\phi^2\delta(1-p)^{2}<br />
D_{2}=\frac{1}{1-\delta}[[q_{d}(x)-\pi-\phi(1-\delta(1-p))]^{2}-\delta[q_{d}(q_{d}(x))-\pi-\phi<br /> p]^{2}]\\+\phi^2\delta(1-p)^{2}<br />
D_{3}=\frac{1}{1-\delta}[[x-\pi-\phi(1-\delta(1-p))]^{2}-\delta[q_{d}(x)-\pi-\phi<br /> p]^{2}]\\+\phi^2\delta(1-p)^{2}

where q_{d}^{-1}(x) is inverse of q_{d}(x) and

q_{a}(x)=\pi+\phi p-\sqrt{\frac{(x-\pi-\phi\delta<br /> p)^{2}}{\delta}+\phi^2p^{2}(1-\delta)}<br />
is real-valued \mathbb{R}\rightarrow\mathbb{R} function.

I already know
q_{d}(\pi)=\pi<br /> and defining q_{d}^{n}(x)=q_{d}(q_{d}^{n-1}(x)) with
q_{d}^{1}(x)=q_{d}(x).

\lim_{n\rightarrow\infty}q_{d}^{n}(x)=\pi<br /> that is successive applications of the q_{d} function converge to
\pi.