Answer to Question #173748 in Complex Analysis for Rayhan

Question #173748

fixed point of f(z) is a complex number z such that f(z)=z. How many fixed points does f(z) have?



 


1
Expert's answer
2021-03-26T16:44:03-0400

We consider the function, "g(z)=f(z)-z." Then the problem reduces to how many zeros does "g" have. Now the number of zeros of an analytic function is discrete and hence countable. So question rises whether it is possible to have a function with finite or countable number of zeros. It is possible. Like "g(z)= e^{z}" has no zeros. Any polynomial of degree "n" has "n" zeros, and functions like "g(z)=sin \\ z" has infinite but countable zeros. So number of zeros or equivalently fixed points are 0 or any finite number or countable.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS