Definition:Concave Real Function/Definition 1

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

$f$ is concave on $I$ :


 * $\forall x, y \in I: \forall \alpha, \beta \in \R_{>0}, \alpha + \beta = 1: \map f {\alpha x + \beta y} \ge \alpha \map f x + \beta \map f y$


 * ConcaveFunction1.png

Also see

 * Equivalence of Definitions of Concave Real Function