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

antonio.pan@uca.es


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