Monday 16 July 2018

Cauchy functional equation three variables

If I have function from $R^3$ to $R$ satisfying



$f(x_1,x_2,x_3)+f(y_1,y_2,y_3) = f(x_1+y_1,x_1+y_2,x_3+y_3)$



is it necessarily linear?




$f(z_1,z_2,z_3) = \lambda _1 z_1+\lambda _2 z_2+\lambda _3 z_3$



Wasn't sure if this was a direct consequence of Cauchy's theorem or not.

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...