Steffensen's inequality is an equation in mathematics named after Johan Frederik Steffensen.[1]
It is an integral inequality in real analysis, stating:
and g : [''a'', ''b''] → [0, 1] is another integrable function, then
| b | |
| \int | |
| b-k |
f(x)dx\leq
| b | |
| \int | |
| a |
f(x)g(x)dx\leq
| a+k | |
| \int | |
| a |
f(x)dx,
where
k=
| b | |
| \int | |
| a |
g(x)dx.