# show that f has a fixed point

• December 3rd 2007, 09:06 PM
hanahou
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:

http://i3.photobucket.com/albums/y57...ty/prob2-1.jpg

Any ideas? Any help is appreciated! thanks
• December 4th 2007, 07:41 AM
ThePerfectHacker
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.