Hi

Let the sequence defined by the value of and where

I am just considering the restriction of f over since it is similar over . You can show that f is decreasing up to and increasing after and

Moreover and

This means that at least from n=2

You can show by induction that

Then

is decreasing (at least from n=2) and higher than therefore converges towards the solution of f(x) = x which is

The only way to get a stationary sequence is

The same for