Functional equation:$f(f(x+y))=f(x)+f(y)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
77071
Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
50833
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
59063
$f(f(x))=f(x)$ question
62111
Functional Equation $f(mn)=f(m)f(n)$.
48925
BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$
32432
Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
155806
(Olympiad Question) $f(2x) + 2f(y) = f(f(x+y))$
74950
Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$