Category:Definitions/Lipschitz Continuity
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This category contains definitions related to Lipschitz Continuity.
Related results can be found in Category: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 "Definitions/Lipschitz Continuity"
The following 4 pages are in this category, out of 4 total.