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convex function

Real function with secant line between points above the graph itself

Entitytype of mathematical functionQ319913

Instance of: type of mathematical function
Subclass of: quasiconvex function
, continuous function
1
Sources
1.Stated in MathWorld
View statement on Wikidata ↗
Part of: concave and convex functions

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph of the function between the two points. Equivalently, a function is convex if its epigraph is a convex set. In simple terms, a convex function graph is shaped like a cup , while a concave function's graph is shaped like a cap .

Overview

All data

24 statements · 33% with external sources · numbers in brackets are citations

Opposite of: concave function
Has characteristic: Jensen's inequality
Defining formula: \forall c, d \in (a, b), t \in [0, 1] : f((1 - t) c + t d) \le (1 - t) f(c) + t f(d)
In defining formula: f symbol represents: convex function

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17 identifiers linking convex function across the web's reference databases

Data quality

statements

33%

externally sourced

Source last edited June 15, 2026. AIDB refreshes this page daily.

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AIDB. (2026). convex function (Q319913). Retrieved from https://aidb.si/e/convex-function-Q319913