Steffensen's inequality is an equation in
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
named after
Johan Frederik Steffensen
Johan Frederik Steffensen (28 February 1873, in Copenhagen – 20 December 1961) was a Danish mathematician, statistician, and actuary who did research in the fields of calculus of finite differences and interpolation. He was professor of a ...
.
It is an
integral
In mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...
inequality in real analysis, stating:
: If ƒ :
'a'', ''b''nbsp;→ R is a non-negative,
monotonically decreasing,
integrable function
: and ''g'' :
'a'', ''b''nbsp;→
, 1is another integrable function, then
::
:where
::
References
External links
*
inequalities
real analysis
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