\begin{definition}[Definition:Convex Real Function/Definition 1]
Let $f$ be a real function which is defined on a real interval $I$.
$f$ is '''convex on $I$''' {{iff}}:
:$\forall x, y \in I: \forall \alpha, \beta \in \R_{>0}, \alpha + \beta = 1: \map f {\alpha x + \beta y} \le \alpha \map f x + \beta \map f y$
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The geometric interpretation is that any point on the chord drawn on the graph of any convex function always lies on or above the graph.
\end{definition}