Jensen's inequality


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Jensen's inequality

[′jen·sənz ‚in·i′kwäl·ədē]
(mathematics)
A general inequality satisfied by a convex function where the xi are any numbers in the region where ƒ is convex and the ai are nonnegative numbers whose sum is equal to 1.
If a1, a2, …, an are positive numbers and s > t > 0, then (a1 s + a2 s + ⋯ + an s )1/ s is less than or equal to (a1 t + a2 t + ⋯ + an t )1/ t .
References in periodicals archive ?
That the raw material would benefit from some purification in the convex region arises naturally from Jensen's inequality which states that for a P(x) function that is convex over [a, b], and for an arbitrary measure with mass density function f(x),
For example, in chapter 1, Jensen's inequality is claimed to state E u(x) [is less than] E(x) (p.