Definition:Lipschitz Condition

Let $$f$$ be a real function.

Let $$I \subseteq \reals$$ be a real interval on which $$\exists A \in \reals: \forall y_1, y_2 \in I: \left|{f \left({y_1}\right) - f \left({y_2}\right)}\right| \le A \left|{y_1 - y_2}\right|$$.

Then $$f$$ satisfies the Lipschitz condition in $$I$$.