If $f:D\to D$ is holomorphic, and has two distinct fixed points, then $f$ is identity
8039
an analytic function from unit disk to unit disk with two fixed point
43136
Branch of the n-th root of a holomorphic function is holomorphic
130872
Map $f: S^n \to S^n$ that extends over $D^{n+1}$ must identify a pair of antipodal points
19750
If a function $f$ is holomorphic on the closed unit disk centered at the origin and is real valued whenever $|z| = 1$, then $f$ is constant.
103125
Show that a non-constant holomorphic function has zeroes in a compact set
115781
Proof about Holomorphic functions in the unit disc
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
106175
A function is analytic if and only if it is holomorphic
143920
zeroes of non-zero holomorphic function form an atmost countable set
46396
When can we find holomorphic bijections between annuli?
141115
$f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$
87723
Show a holomorphic function on unit disc with with $|f'(z) - f'(0)| < |f'(0)|$ is injective
91980
Prove that f is one-to-one on D
26687
Show that $f$ maps the unit circle to itself
138809
Consequences of a fixed point of a bounded, complex analytic function
53848
$f$ holomorphic on $D\setminus \{0\}$ and takes no values in $(-\infty,0],$ then $0$ removable
18763
injective holomorphic function on a convex set