Hey guys, I need to do the following.

Let and let . Show that is Lipschitz continuous for .

My idea is to set , but it is hard to prove that this is a valid Lipschitz constant.

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- February 22nd 2010, 03:29 AMEinStoneLipschitz Continuity
Hey guys, I need to do the following.

Let and let . Show that is Lipschitz continuous for .

My idea is to set , but it is hard to prove that this is a valid Lipschitz constant. - February 22nd 2010, 05:41 AMOpalg
- February 22nd 2010, 06:34 PMDrexel28
What

**Opalg**is just a consequence of a much broader theorem, namely that if is differentiable and is bounded then is Lipschitz. (this is, in fact, an iff statement)

And thus, if is compact and if is continuously differentiable we must have that necessarily bounded and thus is Lipschitz.