Continuity functions (Generalization)

• April 28th 2010, 03:58 PM
rmorin
Continuity functions (Generalization)
A example of function $f:R\to R$ that no satify Lipschitz condition $\lambda$ in all R, but continuous in all R?
• April 28th 2010, 04:09 PM
tonio
Quote:

Originally Posted by rmorin
A example of function $f:R\to R$ that no satify Lipschitz condition $\lambda$ in all R, but continuous in all R?

$f(x)=x^2$ ...(Giggle)

Tonio
• April 28th 2010, 04:17 PM
Drexel28
Quote:

Originally Posted by rmorin
A example of function $f:R\to R$ that no satify Lipschitz condition $\lambda$ in all R, but continuous in all R?

Quote:

Originally Posted by tonio
$f(x)=x^2$ ...(Giggle)

Tonio

Haha!

I bet he meant uniformly continuous, huh?
• April 28th 2010, 04:22 PM
Krizalid
i think it's probably that thing.

but $f(x)=\sqrt x$ on $x\in[0,\infty)$ is a good choice.