Definition:Midpoint-Concave

Definition

Let $f$ be a real function defined on a real interval $I$.

$f$ is midpoint-concave if and only if:

$\forall x, y \in I: \map f {\dfrac {x + y} 2} \ge \dfrac {\map f x + \map f y} 2$

Also see

• Definition:Strictly Midpoint-Concave

• Definition:Midpoint-Convex
• Definition:Strictly Midpoint-Convex

Sources

• 1994: Brian S. Thomson: Symmetric Properties of Real Functions: $\S 4.3$