$f$ be an entire function such that $f(0)=0, f(1)=2$
128547
$f:\mathbb C\rightarrow \mathbb C$ be an arbitrary analytic function satisfying $f(0)=0$ and $f(1)=2.$
77331
$f$ function with $\nabla f=\bar{0}$
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
121771
Proof $f(x)\equiv 0$
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
120774
Show that $f$ has exactly one zero on the square $Q =$ {$x + iy ∈ \Bbb C : |x| < 1, |y| < 1$}.
776
Entire function with positive real part is constant (no Picard)
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
4065
What are the entire functions $f$ such that $|f'(z)| \leq |f(z)| \ ? $
91304
An entire function whose integral is bounded is identically zero
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
134195
Holomorphic function $f:B(0,1) \to B(1,4)$ with $f(0)=3$ and $f(\frac{1}{2})=1$
21954
A question about $f(x)\equiv 0$