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