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 , all of them parameters of the problem. Then

the problem is to find real-valued function

which satisfies

where

where is inverse of and

is real-valued function.

I already know

and defining with

.

that is successive applications of the function converge to

.