Definition:Convex Real Function/Definition 1/Also presented as

Convex Real Function: Definition 1: Also presented as
By setting $\alpha = \lambda$ and $\beta = 1 - \lambda$, this can also be written as:


 * $\forall x, y \in I, x \ne y: \forall \lambda \in \openint 0 1: \map f {\lambda x + \paren {1 - \lambda} y} \le t\lambda \map f x + \paren {1 - \lambda} \map f y$