Let $C \subseteq \mathbb{R}^D$ be a D5623: Convex euclidean real set such that
| (i) | $f : C \to \mathbb{R}$ is a D4364: Real function |
Then the following statements are equivalent
| (1) | $f$ is a D5606: Subconvex real function |
| (2) | \begin{equation} \forall \, \lambda \in [0, 1] : \forall \, x, y \in C : f(\lambda x + (1 - \lambda) y) \leq \lambda f(x) + (1 - \lambda) f(y) \end{equation} |