Jensen's inequality


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 .