Prove that doesnt exist $f$ that $f(0)=1$ and$ |z|^2+1\leq |f(z)|$
74051
No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
105769
Prove that $\exists a, b\in(0,1)$ such that $\int_0^{a} xf(x)dx=0\text{ and }\int_0^bxf(x)dx=\frac{b^2f(b)}{2}.$
123249
An analytic function $f$ on $|z|<1$ with $\sup_{|z|<1} |f(z)|=1$ and $|f(0)|=\frac{1}{2}$ has no zeros in $|z|<\frac{1}{2}$
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
149328
A function such that $f:\mathbb C \to \mathbb C$ such that $f(z)f(iz)=z^2$ satisfies $f(z)+f(-z)=0$.(MADHAVA-2020)
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
28620
Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
148247
Prove the existence of an analytic function
111723
Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
35556
$f(z)=\frac{z}{1+|z|} $ Is 1-1?
8854
Prove $f $ is identically zero if $f(0)=0$ and $|f'(x)|\le|f(x)|$
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
56567
Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
65548
Prove if f(z) is entire function s.t $|f(z)|\leq M|z|$ then $f(z)$ Is polynomial of degree $1$