Be $f$ a Continuous function in $D$ and $f^8$ holomorphic in $D$. Show that $f$ is holomorphic in $D$
132663
Show $f$ is analytic if $f^8$ is analytic
12239
Holomorphic function with a fixed point
109943
Estimates of the value of a holomorphic function and its derivative
155244
Holomorphic self map on the open unit disc
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
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.
62280
If $f:U\to V$ is holomorphic and $f'(z)\neq 0$ for all $z\in U$, then$f$ is locally bijective.
65343
If $f:D\to D’$ is analytic and $u: D'\to R$ is harmonic then the composition of $u$ and $f$ is harmonic in $D$
76485
$f_n(x) \to f(x)$ and $\int |f_n|^2 \, d\mu \to \int |f|^2 \, d\mu$. Use Egorov's theorem to show $f_n \to f$ in $L^2(d\mu)$.
141115
$f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$
12525
complex conjugates of holomorphic functions
134199
Holomorphic function mapping a set onto a straight line
130679
Difference between Analytic and Holomorphic function
133099
Decomposition of holomorphic function as a sum of entire functions
137971
Existence of an holomorphic function
23585
Show that a holomorphic function satisfying $|f(z)|\leq c|z|^n$ must be $f(z)=a\cdot z^n$ for some a.
74622
Composition of holomorphic functions is holomorphic