I try to define a two-variable function $f(x,y) \ge 0$ with both $x,y \in [0,1]$ which satisfies the following constraints:
- $f$ is increasing in both $x$ and $y$
- if $x=0$ then $f(x,y)=0$
- if $y=0$ then $f(x,y)=0$ only if $x=0$
Any suggestion?
I try to define a two-variable function $f(x,y) \ge 0$ with both $x,y \in [0,1]$ which satisfies the following constraints:
Any suggestion?
Would the function $f(x,y)=x(y+1)$ work?