$f$ holomorphic at $B(0,1)$ and $|f(z)|<1$ for every $z\in B(0,1)$ has 2 solutions and $f(z)=z$ Prove for every $z\in B(0,1)$ $f(z)=z$
107072
Schwarz's Lemma, fixed points question
68255
Theorems in complex analysis.
104609
For which $a$ does the equation $f(z) = f(az) $ has a non constant solution $f$
133099
Decomposition of holomorphic function as a sum of entire functions
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
106971
Let $f:U \to V$ be a bijective holomorphic function. Show that inverse of $f$ is also holomorphic.
35378
Prove that $f$ analytic, $f(x) \in \mathbb{R}$ for all $x \in \mathbb{R}$ implies $f(\overline{z})=\overline{f(z)}$
65548
Prove if f(z) is entire function s.t $|f(z)|\leq M|z|$ then $f(z)$ Is polynomial of degree $1$
14759
Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
43136
Branch of the n-th root of a holomorphic function is holomorphic
150124
Holomorphic function such that $f(\frac{1}{n})=\frac{1}{n+1}$.
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
62280
If $f:U\to V$ is holomorphic and $f'(z)\neq 0$ for all $z\in U$, then$f$ is locally bijective.
141115
$f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$
74622
Composition of holomorphic functions is holomorphic
92056
An inequality on holomorphic functions