Steffensen's inequality
Encyclopedia
In mathematics
, Steffensen's inequality, named after Johan Frederik Steffensen
, is an integral
inequality in real analysis. It states that if ƒ : [a, b] → R is a non-negative, monotonically decreasing
, integrable function and g : [a, b] → [0, 1] is another integrable function, then
where
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, Steffensen's inequality, named after Johan Frederik Steffensen
Johan Frederik Steffensen
Johan Frederik Steffensen was a Danish mathematician, statistician, and actuary who did research in the fields of calculus of finite differences and interpolation. He was professor of actuarial science at the University of Copenhagen from 1923 to 1943. Steffensen's inequality and Steffensen's...
, is an integral
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
inequality in real analysis. It states that if ƒ : [a, b] → R is a non-negative, monotonically decreasing
Monotonic function
In mathematics, a monotonic function is a function that preserves the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory....
, integrable function and g : [a, b] → [0, 1] is another integrable function, then
where