Characterize entire functions $f$ such that $|f(z)| \leq |\sin(z)|$
58178
Property of Entire Functions
82371
$f$ is an entire function with Im $f\geq 0$
127887
Existence of a meromorphic functions $f(z)$ such that $|f(z)|\geq |z|$.
139614
Polynomial bounded real part of an entire function
5365
Bound on $|f'(0)|$ of a holomorphic funtion in the unit disk
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
89050
If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
10253
Proving that all entire & injective functions take the form $f = ax + b$?
148486
Suppose $f$ is entire and $|f(z)| \leq A + B |z|^{3/2}$. Show that $f$ is a linear polynomial.
65548
Prove if f(z) is entire function s.t $|f(z)|\leq M|z|$ then $f(z)$ Is polynomial of degree $1$
4084
Does there exist a holomorphic function with the following property?
63255
Proving an entire, complex function with below bounded modulus is constant.
60520
Upper bound for $|f(0)|$ based on its behavior within the unit disk.
148247
Prove the existence of an analytic function
99894
Does there exists an entire function $f$ such that $f(0)=1$ and $|f(z)|\leq \frac{1}{|z|} $ for all $|z|\geq 5$?
122356
Complex Analysis, Entire functions
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$