Prove an entire function is a constant under an inequality
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
76971
Entire functions bounded along $\vert z\vert = R$
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
84103
Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem
114826
Zero Partials imply Constant Function Theorem or Proof
82001
How to prove the function is a constant
97371
Proving a function is constant, under certain conditions?
139614
Polynomial bounded real part of an entire function
89050
If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
776
Entire function with positive real part is constant (no Picard)
90199
Prove that there exists a constant $c>0$ such that the following happens
14067
If f uniformly continous then $|f(x)|\leq C\cdot (1+|x|)$ for constant C
15232
Proving an inequality involving real powers
4065
What are the entire functions $f$ such that $|f'(z)| \leq |f(z)| \ ? $
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
28011
Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?