Namespaces
Variants
Actions

Difference between revisions of "Lipschitz function"

From Encyclopedia of Mathematics
Jump to: navigation, search
(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)
Line 1: Line 1:
Let function $f:[a,b]\to \mathbb R$ such that for some constant M and for all $x,y\in [a,b]$
+
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 $f\in \operatorname{Lip}_M[a,b]$.
+
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=28873