Lipschitz Condition

A function $f(x)$ satisfies the Lipschitz condition of order $\alpha$ at $x=0$ if

$$\vert f(h)-f(0)\vert \leq B\vert h\vert^\beta$$

for all $\vert h\vert < \epsilon$, where $B$ and $\beta$ are independent of $h$, $\beta > 0$, and $\alpha$ is an Upper Bound for all $\beta$ for which a finite $B$ exists.

See also Hillam's Theorem, Lipschitz Function