Lipschitz continuity

Definition

Let $D \subseteq \mathbb{R}$, let $f \colon D \to \mathbb{R}$ be a function, and let $K \ge 0$ be real. The function $f$ is Lipschitz with constant $K$ if $$|f(x) - f(y)| \le K |x - y| \quad \text{for all } x, y \in D.$$ It is Lipschitz if it is Lipschitz with some constant $K$.