Steffensen's inequality
From HandWiki
Revision as of 07:47, 26 December 2020 by imported>Rtexter1 (fix)
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.