Continuous functions, Lifchitz's condition...

Let defined in , continuous by and holds Lifchitz's condition for , in other words: where are points in and is constant. Prove continuous in .

I know that is continuous by (from Lifchitz's condition) and it's given that is continuous by , but now what?

Thank you!

Re: Continuous functions, Lifchitz's condition...

Quote:

Originally Posted by

**Also sprach Zarathustra** Let

defined in

, continuous by

and holds Lifchitz's condition for

, in other words:

where

are points in

and

is constant. Prove

continuous in

.

I know that

is continuous by

(from Lifchitz's condition) and it's given that

is continuous by

, but now what?

Thank you!

Note that for any [tex](x_0,y_0)\in D[tex] you have that now if you make a neighborhood small enough to make the first less than epsilon over two by continuity and the second epsilon/(2A) by the Lipschitz condition you're done.

Re: Continuous functions, Lifchitz's condition...

Re: Continuous functions, Lifchitz's condition...

Quote:

Originally Posted by

**Drexel28** Note that for any [tex](x_0,y_0)\in D[tex] you have that

now if you make a neighborhood small enough to make the first less than epsilon over two by continuity and the second epsilon/(2A) by the Lipschitz condition you're done.

I don't understanding something...

How is that second term is less than epsilon/(2A) by the Lipschitz condition?( \leq A|y_0-y_0|=0 )

Hmmm...(Sleepy)

Re: Continuous functions, Lifchitz's condition...