If $f_1(z), ···, f_n(z)$ are analytic in domain $D$, and continuous to its boundary.
5440
Maximum of sum of finite modulus of analytic function.
40349
Continuity of analytic function implies convergence of power series?
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
16555
If $\mathbb f$ is analytic and bounded on the unit disc with zeros $a_n$ then $\sum_{n=1}^\infty \left(1-\lvert a_n\rvert\right) \lt \infty$
65414
One-one analytic functions on unit disc
71094
Proof that 1-1 analytic functions have nonzero derivative
62901
Bound for Analytic Function on Unit Disk
53726
Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
11062
$f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$ if $\lim_{z\to\infty}f(z)=0$ and $f$ is analytic in $|z|\ge1$
114488
If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.
48619
Let $f$ be a non-constant analytic function on $\mathbb{D}$ satisfying $|f(z^2)| ≤ |f(z)|$ for $|z| < 1.$
51625
Analytic functions close to $\bar{z}$
129073
If $f'$ is bounded, then $f$ is uniformly continuous
68255
Theorems in complex analysis.
80650
Complex differentiability of $f(z)=|z|$
73547
Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?
132663
Show $f$ is analytic if $f^8$ is analytic