I am writing a paper in which I have the following property on a function $f:]0,\infty[^n\to\mathbb R^m$ :
For all $x,y\in]0,\infty[^n$ and any $a\in]0,\infty[$, $f(x+y)=f(x)+f(y)$ and for any $f(ax)=af(x)$.
Which is essentially linearity and implies there is a matrix $A$ such that $f(x)=Ax$ (we can take the limit as a coordinate goes to $1$ and all other go to $0$).
I am wondering what is the appropriate name for this property. Linearity might be confusing, Positive Linearity too. Any idea would be most welcome.