# What do we call function which satistfies $f(x,y,t) \le \vert M(1+\vert x \vert +\vert y \vert)\vert$?

What do we call function which satisfy

$$f(x,y,t) \le \vert M(1+\vert x \vert +\vert y \vert)\vert \text{for all } t \ge 0 \text{and } x,y \in \mathbb{R}$$ (are they sublinear?)

and what about the functions? $$\vert f(x_1,y_1,t)-f(x_2,y_2,t) \vert \le M(\vert x_1-x_2 \vert+\vert y_1-y_2\vert) \text{ for all } t\ge 0,x_1,y_1,x_2,y_2 \in \mathbb{R}$$ (I could say they were lipschitz if $$y_1=y_2$$)

and finally $$\vert g(x_1,y_1,t)-g(x_2,y_2,t) \vert \le M(\sqrt{\vert x_1-x_2 \vert}+\sqrt{\vert y_1-y_2\vert)} \text{ for all } t\ge 0,x_1,y_1,x_2,y_2 \in \mathbb{R}\\ \text{Holder??}$$