Steffensen's inequality

Steffensen's inequality is an equation in mathematics named after Johan Frederik Steffensen. It is an integral inequality in real analysis, stating:

If ƒ : [a, b] → R is a non-negative, monotonically decreasing, integrable function

and g : [a, b] → [0, 1] is another integrable function, then

[math]\displaystyle{ \int_{b - k}^{b} f(x) \, dx \leq \int_{a}^{b} f(x) g(x) \, dx \leq \int_{a}^{a + k} f(x) \, dx, }[/math]

where

[math]\displaystyle{ k = \int_{a}^{b} g(x) \, dx. }[/math]

External links

• Weisstein, Eric W.. "Steffensen's Inequality". http://mathworld.wolfram.com/SteffensensInequality.html.