$f:S^1\to R$ then $\exists z\in S^1$ such that $f(z)=f(-z)$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
28011
Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
123467
Prove that $f(z) = e^z$ maps $\mathbb{C} \setminus B $ onto $\mathbb{C} \setminus \{0\}$.
110643
What are the strategies I can use to prove $f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$?
89257
Give an example of a function $f:\mathbb{R}^2 \mapsto \mathbb{R}^2$ such that
27251
Holomorphic function with $f\circ f=f$
18126
If $f \colon [a,b] \rightarrow \mathbb{R}$, then show that there exists $c \in [a,b]$ such that $\int_a^c f = \int_c^b f$
144539
Power series $ f(g(z)) = z $
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
51395
$f\in L^1(\mathbb{R}) \cap C^1(\mathbb{R})$ and $f'\in L^1(\mathbb{R})$
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
128477
Entire function constant, where $f(z)=f(z+1)$ and $|f(z)|< e^{|z|}$.