Let $ f : \mathbb{C} \rightarrow \mathbb{C} $ such that $ |f(z)| \leq |sin(z)| $ for every $ z \in \mathbb{C}$.
86473
Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.
35378
Prove that $f$ analytic, $f(x) \in \mathbb{R}$ for all $x \in \mathbb{R}$ implies $f(\overline{z})=\overline{f(z)}$
45676
Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
42487
$f(z)$ and $g(z)$ are Meromorphic functions such $|f(z)|\le|g(z)|$ for all $z\in\mathbb{C} $ then $ f=ag$
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
27251
Holomorphic function with $f\circ f=f$
117418
Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation
39492
Finding $z\in \mathbb C$ with $\sin z = 2$?
143072
Proving $|\sin x - \sin y| < |x - y|$
65297
Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2} \right |\leq \left |b-c \right |$.
68409
Consider $f(x,y)=\sup_{θ,φ}\{||e^{i θ }x+ e^{i φ }y||^2: θ,φ∈R\}$ in which $x,y\in\mathbb C^n$
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
20955
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
56978
How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
46514
Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic