1)Let be a continous function on solve the functional equation: .

Results 1 to 8 of 8

- Nov 18th 2007, 04:59 PM #1

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- Nov 18th 2007, 05:26 PM #2

- Nov 18th 2007, 05:33 PM #3

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- Nov 18th 2007, 05:50 PM #4

- Nov 20th 2007, 05:21 AM #5

- Joined
- Nov 2007
- Posts
- 33

Let be a positive integer. Then

So

Now let be a positive rational number. Then

Now let be a positive real number. By continuity,

where the last result is established by our definition of over the rational numbers.

Assume , then it is trivial that . Thus, for any positive real number ,

Therefore, for all or assume , then it is trivial that for all

- Nov 20th 2007, 11:22 AM #6

- Joined
- Nov 2007
- Posts
- 33

- Nov 21st 2007, 08:42 AM #7

- May 26th 2009, 08:39 PM #8