Does there exists a transcendental entire function having no fixed points?

Question

I think yes, there exist a transcendental entire function having no fixed point...

As I take $ f(z) = e^z + 1$

Is it true or false?

https://math.stackexchange.com/q/450420/4890 – user541686 Mar 19 '18 at 07:09 — user541686, Mar 19 '18 at 07:09

score 10 · Accepted Answer · edited Mar 19 '18 at 08:36

10

It should be $$ e^z + z $$ because $e^z + z = z$ implies...

edited Mar 19 '18 at 08:36

Peter Mortensen

answered Mar 19 '18 at 01:57

Will Jagy

im not getting @will jagy,,,can u elaborate more ??? – jasmine Mar 19 '18 at 01:59
@lomber: You want to check if $f(z) = e^z + z$ has a fixed point. Having a fixed point means that $z = f(z) = e^z + z$ which implies $e^z = 0$. Does it have a solution? – user541686 Mar 19 '18 at 07:08
thanks a lots @Mehrdad – jasmine Mar 19 '18 at 08:24

1 Answers1