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 ::

\int_^ f(x) \, dx \leq \int_^ f(x) g(x) \, dx \leq \int_^ f(x) \, dx,

:where ::

k = \int_^ g(x) \, dx.

References

External links

* inequalities real analysis {{mathanalysis-stub