Category:Convex Real Functions

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This category contains results about Convex Real Functions.
Definitions specific to this category can be found in Definitions/Convex Real Functions.

$f$ is convex on $I$ if and only if:

$\forall x, y \in I: \forall \alpha, \beta \in \R_{>0}, \alpha + \beta = 1: f \left({\alpha x + \beta y}\right) \le \alpha f \left({x}\right) + \beta f \left({y}\right)$

Also see

Category:Concave Real Functions