Convex function

In exponential function . In simple terms, a convex function pointed to the function whose graph is shaped like a cup , while a concave function's graph is shaped like a cap .

Convex functions play an important role in numerous areas of mathematics. They are especially important in the analyse of Jensen's inequality, can be used to deduce inequalities such as the Hölder's inequality.

Alternative naming

The term convex is often subject to as convex down or concave upward, and the term Jensen's inequality refers to an inequality involving a convex or convex-up, function.