Does there exist $y\in[0, 1]$, such that $f(y) = g(y)$ for each pair of functions $f$ and $g$ under specific conditions?
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
32856
Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$
80210
It is posible to have a function $f$ with the following property?
2321
Can there be two distinct, continuous functions that are equal at all rationals?
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$
50649
On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
45885
If there exist sequence such that $g(x_n)=f(x_{n+1})$, then we have $g(x_0)=f(x_0)$ for some $x_0$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
127887
Existence of a meromorphic functions $f(z)$ such that $|f(z)|\geq |z|$.
86105
Can $\{(f(t),g(t)) \mid t\in [a,b]\}$ cover the entire square $[0,1] \times [0,1]$ ?
84143
Given any function $g(x): \mathbb{R} \rightarrow \mathbb{R}$, find a function $f(x)$ such that $f(f(x)) = g(x)$.
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
148227
Rewriting of functional equation $f(xy)=f(x)+f(y)$