f and g are entire and $ \left|f(z)\right| \leq \left|g(z)\right| $ then $\exists \alpha\in \mathbb{C}$ such that $f(z)=\alpha g(z)$
98399
Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.
64905
Let $f \in C [a,b]$ such that $\forall x\exists y$ such that $|f(y)| \leq \frac{1}{2}|f(x)|$. Prove that $\exists c\in [a,b]$ such that $f(c) = 0$.
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
84206
How do I show that if $f$ is entire and $\{\lvert f(z)\rvert < M\}$ is connected for all $M$, then $f$ is a power function?
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
48780
How t show $f=g$ almost everywhere
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
4065
What are the entire functions $f$ such that $|f'(z)| \leq |f(z)| \ ? $
124309
$g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
139667
Show that $f(z) = cg(z)$ is valid for two analytic functions $f$ and $g$ given a certain relationship between them
4296
If $f,g$ are entire functions and$\ fg\equiv 0$ then either $f \equiv 0$ or $g\equiv0. $
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
99630
For every $g\in G$ there exists an $h\in G$ such that $g = h^3$
135441
When is $\mathbb{Z}[\alpha]$ dense in $\mathbb{C}$?
105455
Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement