Show that $|\int_C f(z)| \leq 4$
53726
Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
61466
what is $\int_{|z|=3}\frac{1}{(z-2)^n(z-4)^m}dz$ for $m,n\in\mathbb{N}$?
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
126736
Show that $\lim_{\epsilon\to0^{+}}\frac{1}{2\pi i}\int_{\gamma_\epsilon}\frac{f(z)}{z-a} \, dz=f(a)$
87723
Show a holomorphic function on unit disc with with $|f'(z) - f'(0)| < |f'(0)|$ is injective
95626
$\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
158180
An inequality of $\int_0^1 |f(x)|dx$
153855
Complex analysis, showing a function is constant
56967
Show that $ f^2 − g^2 = C $ for some real constant C
139453
Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$
128189
Proving Integral Inequality
28399
Showing $f$ is constant
158561
Let $f (z) $ be an entire function such that $|f (z)|≤K|z|$, $∀z∈\mathbb{C}$, for some $K>0$. If $f (1) =i$, then$f (i) $ is
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
60520
Upper bound for $|f(0)|$ based on its behavior within the unit disk.
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$