lipschitz continuity
a function Rn→Rm is locally lipschitz continuous at a point ˆx if
d(f(xi),f(x2))≤Ld(x1,x2)∀x1x2∈B(ˆx∈Rn,δ)∃δ>0∃L>0
Where B is the open ball, L is the lipschitz constant, and d is some measure of distance, typically the euclidean norm.
In a sense, this means that L is an upper bound on the change in distance between two points after being transformed by the function.
If the function is locally lipschitz continuous at all points ˆx∈R then we say it is globally lipschitz continuous.