holomorphic function $f$ in $\overline{B(0,1)}$ has nonzero derivative at the maximal value point.
129399
Maximum module principle
129324
Let $f:[0;1]\to\mathbb R$ be continiously differentiable
113888
Behavior of derivative near the zero of a function.
143920
zeroes of non-zero holomorphic function form an atmost countable set
38427
Holomorphic function $\varphi$ with fixed point $z_0$ such that $\varphi'(z_o)=1$ is linear?
134199
Holomorphic function mapping a set onto a straight line
155244
Holomorphic self map on the open unit disc
94680
Holomorphic function $f$ such that $f'(z_0) \neq 0$
44458
Uniform limit of holomorphic functions
119477
Understanding the Definition of $\int_\gamma f\ \overline{dz}$
83014
Holomorphic function interpolating $e^{-n}$
15378
Why a holomorphic function satisfying these conditions has to be linear?
95632
Where is this function holomorphic?
12239
Holomorphic function with a fixed point
134195
Holomorphic function $f:B(0,1) \to B(1,4)$ with $f(0)=3$ and $f(\frac{1}{2})=1$
106971
Let $f:U \to V$ be a bijective holomorphic function. Show that inverse of $f$ is also holomorphic.
40336
Existence of Holomorphic function (Application of Schwarz-Lemma)