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Difference between revisions of "Lipschitz function"

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(Created page with "Let function $f:[a,b]\to \mathbb R$ such that for some constant M and for all $x,y\in [a,b]$ \begin{equation}\label{eq:1} |f(x)-f(y)| \leq M|x-y|. \end{equation} Then function...")
 
m (wording)
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Let function $f:[a,b]\to \mathbb R$ such that for some constant M and for all $x,y\in [a,b]$
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Let a function $f:[a,b]\to \mathbb R$ be such that for some constant M and for all $x,y\in [a,b]$
 
\begin{equation}\label{eq:1}
 
\begin{equation}\label{eq:1}
 
|f(x)-f(y)| \leq M|x-y|.
 
|f(x)-f(y)| \leq M|x-y|.
 
\end{equation}
 
\end{equation}
Then function $f$ is called Lipschitz on $[a,b]$ or one writes $f\in \operatorname{Lip}_M[a,b]$.
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Then the function $f$ is called Lipschitz on $[a,b]$, and one writes $f\in \operatorname{Lip}_M[a,b]$.

Revision as of 16:31, 24 November 2012

Let a function $f:[a,b]\to \mathbb R$ be such that for some constant M and for all $x,y\in [a,b]$ \begin{equation}\label{eq:1} |f(x)-f(y)| \leq M|x-y|. \end{equation} Then the function $f$ is called Lipschitz on $[a,b]$, and one writes $f\in \operatorname{Lip}_M[a,b]$.

How to Cite This Entry:
Lipschitz function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lipschitz_function&oldid=28813