Let $f:\mathbb C\to\mathbb C$ is entire function. And $f(z+1)=f(z)$ and $f(z+i)=f(z)$ then what can you say about $f$?
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?
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
86473
Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.
36379
Suppose that $ f $ is entire and that for each $ z $, either $ |f(z)| \leq 1 $ or $ |f^\prime (z) |\leq 1 $. Prove that $ f $ is a linear polynomial.
4296
If $f,g$ are entire functions and$\ fg\equiv 0$ then either $f \equiv 0$ or $g\equiv0. $
56628
If $f: D(0,1)\to \mathbb C$ is holomorphic, then there is a sequence $\{z_n\}$ in $D(0,1)$ such that $|z_n| \to 1$ and $\{f(z_n)\}$ is bounded
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
128547
$f:\mathbb C\rightarrow \mathbb C$ be an arbitrary analytic function satisfying $f(0)=0$ and $f(1)=2.$
146506
If a complex function $f$ is Entire, and there exist $k,R > 0$, $n \in N$ such that $|f(z)| > k|z|^n$ for all $|z| > R$, then f is a polynomial.
133386
If $f$ is entire and $\lim_\limits{z\to\infty} \frac{f(z)}{z} = 0$ show that $f$ is constant
59063
$f(f(x))=f(x)$ question
113687
$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
4065
What are the entire functions $f$ such that $|f'(z)| \leq |f(z)| \ ? $
62568
Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
101773
Let $g : A \to B$ and $f : B \to C$ be functions. Let $f \circ g$ be onto. Are both $f$ and $g$ necessarily onto?