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

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- Nov 18th 2007, 05:59 PM #1

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- Nov 18th 2007, 06:26 PM #2

- Nov 18th 2007, 06:33 PM #3

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- Nov 18th 2007, 06:50 PM #4

- Nov 20th 2007, 06:21 AM #5

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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, 12:22 PM #6

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- Nov 21st 2007, 09:42 AM #7

- May 26th 2009, 09:39 PM #8