lipschitz continuity

Lipschitz Continuity

A function $f$ is Lipschitz continuous if there exists a constant $k$ such that for any two points $x_1$ and $x_2$:

$$|f(x_1)-f(x_2)|\le k|x_1-x_2|$$

This means the function can’t change faster than some fixed rate $k$ - it puts a bound on how quickly the function can vary.