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
\( {\displaystyle \int _{b-k}^{b}f(x)\,dx\leq \int _{a}^{b}f(x)g(x)\,dx\leq \int _{a}^{a+k}f(x)\,dx,} \)
where
\( {\displaystyle k=\int _{a}^{b}g(x)\,dx.} \)
External links
Weisstein, Eric W. "Steffensen's Inequality". MathWorld.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
