Webband its reverse version. We also sharpen Jensen's inequalities for positive isotonic linear functionals. 1. Introduction. In the articles [1] and [2] sharpenings of the inte-gral versions of Holder's and Jensen's inequalities were obtained. Here we improve these results using a positive isotonic functional leading WebbJensen’s inequality is a fundamental inequality in mathematics anditunderliesmanyimportantstatisticalproofsandconcepts. …

Sharpening Hölder

WebbThe widely used Jensen’s inequality for convex functions, attributed to Danish mathematician Johan Jensen, dates back to 1906[12]. The literature contains numerous bounds on the Jensen gap, defined as J (f,X ∼ P) = E[f (X)] − f (E[X]), where X is a random variable with distribution P, and the function f might be convex or nonconvex [20]. tryphaina site ok

[1707.08644] Sharpening Jensen

Webb1 sep. 2024 · This post is all about Jensen’s inequality, an elementary but powerful result about convex functions. It comes up all over the place in mathematics, probably because the concept of convexity is itself so fundamental. I ran into it recently as I was thinking about relative entropy and why it is so well behaved; I think a lot of it comes down to the … Webbelifesciences.org WebbNow, by Jensen’s inequality with weights 1 = = n= 1 n, we have 1 n x 1 p 1 x 1 + x 2 p 1 x 2 + + x n p 1 x n f x 1 + x 2 + + x n n = f 1 n = 1=n p 1 1=n which simpli es to the inequality we wanted. 2.4 The AM-GM inequality The rst example we did can be generalized to a result called the AM-GM (Arithmetic Mean-Geometric Mean) inequality. It ... phillip island linen hire