MathDB

Very concex function

Source: USAM0 2000 #1 (billzhao)

August 8, 2005

functionUSA(J)MOUSAMOinductionalgebra

Problem Statement

Call a real-valued function

f

very convex if \frac {f(x) \plus{} f(y)}{2} \ge f\left(\frac {x \plus{} y}{2}\right) \plus{} |x \minus{} y| holds for all real numbers

x

and

y

. Prove that no very convex function exists.