Show that $h$ is entire and $f$ is a constant function.
132657
Function $ f $ defined on unit disk $ D $ has real values on $ \partial D $, why is $ f $ real valued?
153855
Complex analysis, showing a function is constant
154034
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
105172
Prove that the entire function is constant over certain conditions.
82367
Prove that a holomorphic function with postive real part is constant
11322
Show that $f$ vanishes identically.
82371
$f$ is an entire function with Im $f\geq 0$
32789
Show bounded harmonic function on $\mathbb{C}$ is constant.
137043
To show that function is constant
39386
Harmonic non-surjective functions are constant
7755
Question on entire function
56978
How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
135772
how to show image of a non constant entire function is dense in $\mathbb{C}$?
64172
Show that if $f$ is analytic in a domain $D$ and $|f(z)|$ is constant in $D$, then the function $f(z)$ is constant in $D$
10727
Let $f$ be an entire function and $L$ a line in $\mathbb{C}$ such that $f(\mathbb{C})\cap L=\emptyset$. Show that $f$ is constant function.
133386
If $f$ is entire and $\lim_\limits{z\to\infty} \frac{f(z)}{z} = 0$ show that $f$ is constant
73547
Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?