$f(f(x)^2+f(y))=xf(x)+y$
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
60348
How do I prove $F(a)=F(a^2)?$
144090
How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
14975
Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
6680
Solve for all possible functions f: $|f(x)-f(y)|=2|x-y|$.
86128
Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
24862
Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
17175
Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$
76458
Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
104263
How to show that $f'(x)<2f(x)$
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $