Existence entire function $f$ such $|\bar{z} - f(z)| < 1$ for $|z| = 1$
51625
Analytic functions close to $\bar{z}$
151958
How to show $f'(0)$ exist and is equal to $1$?
74245
Characterizing non-constant entire functions with modulus $1$ on the unit circle
58178
Property of Entire Functions
127887
Existence of a meromorphic functions $f(z)$ such that $|f(z)|\geq |z|$.
15001
Multiple choice question: Let $f$ be an entire function such that $\lim_{|z|\rightarrow\infty}|f(z)|$ = $\infty$.
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
153510
Questions about the existence of a function
55138
An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
74051
No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
147270
Entire function. Prove that $f(\bar{z})=\overline{f(z)}, \forall z\in C$
28620
Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
62568
Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
26353
Can any harmonic function on $\{z:0<|z|<1\}$ be extended to $z=0$?
42095
Existence in ZF of a set with countable power set