"monotonic" is well defined for functions $f(x)$, where e.g. $x\in[0,1]$ and $f(x)\in\mathcal{R}$. The quality I particularly care about is that if $f(x)$ is monotonic then it will not have any local extrema for $x\in(0,1)$.

Is there an analogous word for a function $g(x,y)$ with $x,y\in[0,1]$ and $g(x,y)\in\mathcal{R}$, where $g(x,y)$ has no local extrema for $x,y\in(0,1)$?

"monotonic" is well defined for functions $f(x)$, where e.g. $x\in[0,1]$ and $f(x)\in\mathbb{R}$. The quality I particularly care about is that if $f(x)$ is monotonic then it will not have any local extrema for $x\in(0,1)$.

Is there an analogous word for a function $g(x,y)$ with $x,y\in[0,1]$ and $g(x,y)\in\mathbb{R}$, where $g(x,y)$ has no local extrema for $x,y\in(0,1)$?