The functional equation $f(xy)=f(x)f(y)$
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
147195
Help needed in finding the value of $f(2001)$ in the given functional equation
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$
88683
Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
25953
Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
55693
The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $
88311
Linear functional f(v)=0 imply v=0
68409
Consider $f(x,y)=\sup_{θ,φ}\{||e^{i θ }x+ e^{i φ }y||^2: θ,φ∈R\}$ in which $x,y\in\mathbb C^n$
16948
Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
132093
Solve $f(f(x))=f(x)$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
153942
Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
86128
Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
76458
Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
102175
$Z=XY$, $E_Z[Z]$, $E_{X,Y}[XY]$
48652
Solve the functional equation $2f(x)=f(ax)$ for some $a$.