Category:Lipschitz Continuity

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This category contains results about Lipschitz Continuity.
Definitions specific to this category can be found in Definitions/Lipschitz Continuity.

Let $M = \struct {A, d}$ and $M' = \struct {A', d'}$ be metric spaces.

Let Let $f: A \to A'$ be a mapping.


Then $f$ is a Lipschitz continuous mapping if and only if there exists a positive real number $K \in \R_{\ge 0}$ such that:

$\forall x, y \in A: \map {d'} {\map f x, \map f y} \le K \map d {x, y}$

That is, the distance between the images of two points lies within a fixed multiple of the distance between the points.

Pages in category "Lipschitz Continuity"

The following 2 pages are in this category, out of 2 total.