Steffensen's inequality

Steffensen's inequality is an equation in mathematics named after Johan Frederik Steffensen.[1]

It is an integral inequality in real analysis, stating:

If ƒ : [ab] → R is a non-negative, monotonically decreasing, integrable function
and g : [ab] → [0, 1] is another integrable function, then
where
  1. ^ Rabier, Patrick J. (2012). "Steffensen's inequality and estimates of weighted integrals". Proceedings of the American Mathematical Society. 140 (2): 665–675. doi:10.1090/S0002-9939-2011-10939-0. ISSN 0002-9939.