# Definition:Strictly Midpoint-Convex

## Definition

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

$f$ is strictly midpoint-convex if and only if:

$\forall x, y \in I : f \left({\dfrac {x + y} 2}\right) < \dfrac {f \left({x}\right) + f \left({y}\right)} 2$