Hi

I need to show that a real valued (defined on R) upper bounded convex function must be a constant.

Thanks

Mark

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- Aug 22nd 2007, 01:49 AMMark84Upper bounded convex funtion
Hi

I need to show that a real valued (defined on R) upper bounded convex function must be a constant.

Thanks

Mark - Aug 22nd 2007, 03:49 AMJakeD
- Aug 22nd 2007, 04:09 AMMark84
- Aug 22nd 2007, 04:21 AMJakeD
- Aug 22nd 2007, 05:06 AMMark84
- Aug 22nd 2007, 06:00 AMJakeD
- Aug 22nd 2007, 06:20 AMMark84
Thanks for all the help

/Mark - Aug 22nd 2007, 06:30 AMmathisfun1
Here's another approach which I find more intuitive. Let M be an upper bound and suppose there exists a<b such that f(a)<f(b)<M. Convexity tells us that . There is some such that . Since for some we have , by convexity we must have for all . For , - contradiction.