Difference between revisions of "Lipschitz function"
From Encyclopedia of Mathematics
(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 $[a,b]$ | + | 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
Lipschitz function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lipschitz_function&oldid=28813