Julián Aguirre gave a simple-amazing answer for this question: How to prove this property using convexity?
Unfortunately, i don't understand how to deduce the last inequality $a+b-c<(a+b)/2$.
Somebody help me. I don't know what I'm missing.
2026-05-15 19:04:37.1778871877
How to deduce the last inequality ;(
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He is trying to show that if the result is true for all convex functions (with no assumption on monotonicity if $f''$ then there is another convex function $g$ for which the new $c$ (which is $a+b-c$) is less than $\frac {a+b} 2$. Hnec the result cannot be true with just convexity.