Lipschitz continuous function

Definition

It is a function $f : (X, d_{X}) \to (Y, d_{Y})$ between two metric spaces which satisfies

d_{Y} (f (a), f (b)) \leq K \cdot d_{X} (a, b)

being $K > 0$ constant.

Remark

Not every continuous function is Lipschitz continuous. For example $f (x) = \sqrt{x}$ .

Related

uniformly continuous function

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Author of the notes: Antonio J. Pan-Collantes

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