Lipschitz continuous

[[concept]]

lipschitz stable / continuous

A function $f:x\to y$ is $c-$Lipschtiz stable/continuous if $||f(x)-f(x^{\prime })||\le c||x-x^{\prime }||\forall x,x^{\prime }$ or if $||f^{\prime }(x)||\le c\forall x$

If $T$ is a bounded linear operator, then $T$ is Lipschitz with $c=||T|{|}_{\text{op}}$, where $||\cdot |{|}_{\text{op}}$ is the operator norm.

References

References

See Also

Mentions

Mentions

const modules = await cJS()
 
const COLUMNS = [  
	{ id: "Name", value: page => page.$link },  
	{ id: "Last Modified", value: page => modules.dateTime.getLastMod(page) },
];  
  
return function View() {  
	const current = dc.useCurrentFile();
// Selecting `#game` pages, for example. 
	let queryString = `@page and linksto(${current.$link})`;
	let pages = dc.useQuery(queryString);
	
	// check types
	pages = pages.filter( (p) => !modules.typeCheck.checkAll(p, current) ).sort()
	
	
	return <dc.Table columns={COLUMNS} rows={pages} paging={20}/>;  
}  

const { dateTime } = await cJS()
 
return function View() {
	const file = dc.useCurrentFile();
	return <p class="dv-modified">Created {dateTime.getCreated(file)}     ֍     Last Modified {dateTime.getLastMod(file)}</p>
}