Lipschitz continuous function

Definition

It is a function f:(X,dX)(Y,dY) between two metric spaces which satisfies

dY(f(a),f(b))KdX(a,b)

being K>0 constant.

Remark

Not every continuous function is Lipschitz continuous. For example f(x)=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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