Definition:Convex Real Function

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

Also known as
A convex function can also be referred to as:
 * a concave up function
 * a convex down function

Also see

 * Equivalence of Definitions of Convex Real Function


 * Definition:Strictly Convex Real Function


 * Definition:Concave Real Function
 * Definition:Strictly Concave Real Function


 * Compare concave function. It is immediately obvious from the definition that $f$ is convex on $I$ iff $-f$ is concave on $I$.