# Thread: show that f has a fixed point

1. ## show that f has a fixed point

I think I am supposed to use Rouche Theorem and Cauchy Argument Principle for this problem as well:

Any ideas? Any help is appreciated! thanks

2. Define $g(z) = f(z) - z$ and use Rouche's theorem by showing that $g(z)$ has a zero in the disk. That will mean there is $a\in D(0,1)$ such that $g(a)=0\implies f(a) = a$ and hence $f$ has a fixed point.