Lipschitz continuity (Lipschitz continuity)

Lipschitz continuity Lipschitz continuity

DEFINITION 1. $A$ function $f$ from $S \subset \mathbb{R}^{n}$ into $\mathbb{R}^{m}$ is Lipschitz continuous at $x \in S$ if there is a
constant $C$ such that
$\|f(y)-f(x)\| \leq C\|y-x\|$
for all $y \in S$ sufficiently near $x$ .

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