# 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 ?
When dealing with integral terms which are generated in the process of functional derivation, one common point of the above reference is the use of Jensen's inequality. Jensen's inequality is simple and convenient, but it has a certain conservation.
Sababheh, "Improved Jensen's inequality," Mathematical Inequalities & Applications, vol.
Then by using Jensen's Inequality, we show that FUH cannot simultaneously hold true for both the sellers and buyers of the same forward currency contracts.
The proof is based on the multiplier method and makes use of some properties of convex functions including the use of the general Young's inequality and Jensen's inequality. The paper is organized as follows.
Torres, "Diamond-a Jensen's inequality on time scales," Journal of Inequalities and Applications, vol.
Based on combination of Leibniz-Newton formula, free-weighting matrices, Cauchy's inequality, modified version of Jensen's inequality, decomposition technique of coefficient matrix, the use of suitable parameter-dependent Lyapunov-Krasovskii functional, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria for these systems will be obtained in terms of LMIs.
However, this can be difficult, so we will upper bound this by using the Jensen's inequality and a numerical method.
By Proposition 1, (1.2) and Jensen's inequality we obtain
The three are variants of Jensen's inequality. The first inequality is a comparison of the expected value of a ratio to the ratio of the expected value, a problem that arises in pricing foreign exchange rates.
When the risk-free rate is time varying, Jensen's inequality implies that the expected value of the conditional alpha in the beta pricing model is not the unconditional alpha.
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