Jensen's inequality (redirected fromJensen inequality) [′jen·sənz ‚in·i′kwäl·ədē] (mathematics) A general inequality satisfied by a convex function where thexiare any numbers in the region where ƒ is convex and theaiare nonnegative numbers whose sum is equal to 1. ...
The Jensen inequality is established for a lower semicontinuous convex functional defined on an ideal Banach space with order continuous norm.
Jensen's inequality for multivariate medians Given a probability measure μ on Borel sigma-field of R d , and a function f : R d ↦ R , the main issue of this work is to establish inequalities of th... M Merkle - 《Journal of Mathematical Analysis & Applications》...
Gruss inequalityJensen inequalityLipschitz conditionZipf-Mandelbrot lawIn this paper, we prove several Jensen-Gruss type inequalities under various conditions. Some applications in information theory are also given.Butt, Saad IhsanKlaricic Bakula, MilicaPecaric, DildaPecaric, Josip...
Jensen's inequality in the calculus of variations 来自 Semantic Scholar 喜欢 0 阅读量: 29 作者: Pablo Pedregal 摘要: We propose and describe an alternative perspective for the study of systems of boundary value problems governed by ODEs. It is based on a variational approach that seeks to ...
Chicago/Turabian Style Chu, Yu Ming, Baloch, Imran Abbas, Haq, Absar Ul, Sen, Manuel De La. "The Jensen's inequality and functional form of Jensen's inequality for 3-convex functions at a point." Journal of Mathematics and Computer Science, 22, no. 2...
The Best Lower Bound Depended on Two Fixed Variables for Jensen's Inequality with Ordered Variables 喜欢 0 阅读量: 41 作者: Vasile Cirtoaje 摘要: Let x = {x_1,x_2,…,x_n}eequencefeal numberselongingon interval I,nd let p = {p_1,p_2,…,p_n}eequencef given positive weightss...
We give the best lower bound for the weighted Jensen's discrete inequality with ordered variables applied to a convex function <img src="https://static-content.springer.com/image/art%3A10.1155%2F2010%2F128258/MediaObjects/13660_2010_Article_2056_IEq1_HTML.gif" alt="https://static-content.spr...
(probability or integral) Jensen inequality can be used to derive lower bounds for this central function. Specifically, we propose alternative proofs for two existing results and establish new lower bounds. In particular, they have the properties of being applicable to all positive real numbers and...
The Jensen Inequality Let(设)fbe a function with a positive second derivative(二阶导数). Such a function is called “convex"(凸的,注意是向下凸,向上凹,如 x2) and satisfies theinequality (1) inequation (1) relates a function of an average to an average of the function. The average can ...