Functional equation $f(ax)=bf(x)$
48652
Solve the functional equation $2f(x)=f(ax)$ for some $a$.
34074
Nonlinear Functional Equation $f(x)^{2}=f\left(\frac x a\right)$
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
88311
Linear functional f(v)=0 imply v=0
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
146719
Functional equation $f(r \cos \varphi)+f(r \sin \varphi)=f(r)$
24862
Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
103934
Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$
71156
$f(x) = \frac {ax+b}{cx+d}$ , bijection $f: \Bbb R \to\Bbb R$?
32856
Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$
144090
How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$
144656
Linear functional and a bounded norm
72006
Suppose $f(x)$ is linear i.e. $f(x + y) = f(x) +f(y) $ and monotone on $[-\infty, +\infty]$, then $f(x) = ax$, a real.
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
59063
$f(f(x))=f(x)$ question
67594
Books on functional equations
19019
Find all functions $f:\Bbb{Q}\rightarrow \Bbb{Q}$ such that $f(x)+f(t)=f(y)+f(z)$ for all rational numbers $x<y<z<t$ that form an AP