Sharpening jensen's inequality

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August undefined, 2024

WebbRefinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory Yongping Deng ,1 Hidayat Ullah ,2 Muhammad Adil Khan ,2 Sajid Iqbal ,3 and Shanhe Wu 1 1DepartmentofMathematics,LongyanUniversity,Longyan364012,China 2DepartmentofMathematics,UniversityofPeshawar,Peshawar25000,Pakistan Webb至于《数学分析》中对于函数凹凸的定义，也是由于历史原因有诸多版本。. 有兴趣的读者可以看看数学分析，而本文更侧重于Jensen inequality. 我们说. f（x）’>0\Leftrightarrow f（x）函数增. f（x）’<0\Leftrightarrow f（x）函数减. 以上内容初一甚至更早大家已经有所 …

Jensen

WebbThis article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, … WebbAbstract This article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate results in spite of its simple form. chucklefish strategy bundle

About the sharpness of the Jensen inequality - PubMed

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 … In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder … Visa mer The classical form of Jensen's inequality involves several numbers and weights. The inequality can be stated quite generally using either the language of measure theory or (equivalently) probability. In the … Visa mer Form involving a probability density function Suppose Ω is a measurable subset of the real line and f(x) is a non-negative function such that $${\displaystyle \int _{-\infty }^{\infty }f(x)\,dx=1.}$$ Visa mer • Jensen's Operator Inequality of Hansen and Pedersen. • "Jensen inequality", Encyclopedia of Mathematics, EMS Press, 2001 [1994] • Weisstein, Eric W. "Jensen's inequality". MathWorld. Visa mer Jensen's inequality can be proved in several ways, and three different proofs corresponding to the different statements above will be offered. Before embarking on these … Visa mer • Karamata's inequality for a more general inequality • Popoviciu's inequality • Law of averages • A proof without words of Jensen's inequality Visa mer chuckle fish new game

EconPapers: Sharpening Jensen

http://ele-math.com/static/pdf/books/17689-MIA19.pdf Webb3 sep. 2024 · Jensen’s Inequality is a useful tool in mathematics, specifically in applied fields such as probability and statistics. For example, it is often used as a tool in … chucklefish projectsWebbFurther sharpening of Jensen's inequality Sang Kyu Lee a Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA View further author … chucklefish reddit

"WebbIn particular, just as the Jensen inequality becomes an equality when ϕ is linear, for the new inequality we obtain an equality also when ϕ is quadratic. At the heart of the paper is an apparent new technique for improving classical inequalities based on nonlinear functions. MSC codes analytic function convex function Jensen gap power series " - Sharpening jensen's inequality

Sharpening jensen's inequality

WebbThe main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green … Webb琴生不等式（英語： Jensen's inequality ，台湾稱作簡森不等式 [1] ），或稱延森不等式，以丹麥數學家約翰·延森命名。它給出積分的凸函數值和凸函數的積分值間的關係，在此不等式最簡單形式中，闡明了對一平均做凸函數轉換，會小於等於先做凸函數轉換再平均。若將簡森不等式應用在二點上，就回到了凸函數的基本性質：过一个凸函数上任意 …

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WebbProving Holder's inequality using Jensen's inequality. Asked 9 years, 4 months ago. Modified 7 years, 11 months ago. Viewed 5k times. 6. Let p and q be positive reals such … WebbUnder certain conditions, it is an ultimate bound equal to the Jensen gap. To the best of our knowledge, this is the first such bound to be developed. The proposed bound is applied to moment generating functions, the inequality of arithmetic and geometric means, a power mean, and information entropy.

Webb6 mars 2024 · In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the … WebbDive into the research topics of 'Sharpening Jensen's Inequality'. Together they form a unique fingerprint. Sort by Weight Alphabetically Mathematics. Jensen's inequality 74%. Power Mean 38%. Moment generating function 34%. Presentation 24%. Calculus 23%. Form 12%. Business & Economics. Jensen's Inequality 100%. Moment ...

Webb3 sep. 2024 · In this study, we propose a new bound for Jensen's inequality. Under certain conditions, it is an ultimate bound equal to the Jensen gap. To the best of our … WebbThe main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green …

WebbThe inequality (1.5)is appropriate for iteration, using a sequence of functions. e. 1, e. 2, e. 3, ..., as in the case of Bessel’s inequality, but if. c. θ,r < 1 there is an exponential decay of the coeﬃcients in the analogue of Bessel’s inequality. We note that the inequality (1.5)holds trivially for. c. θ,r =0by Hölder’s inequality ...

WebbThe main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green functions and considerin desk and chair or kyphosisWebb12 nov. 2024 · The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric means or the Hölder inequality. desk and chair for home officeWebbvide a more general reﬁnement of integral Jensen’s inequality. We establish a reﬁnement of discrete Jensen’s inequality concerning certain tuples and give applications to different means. Finally, we give applications of discrete main result in information theory and providea more generalreﬁnement of discrete Jensen’s inequality. desk and chair online usedWebb25 maj 2024 · The proof of Proposition 3.1 is based on Jensen’s inequality, but the reduction to constants is not obtained by applying Jensen’s inequality to show that … chucklefish rustWebbSharpening Jensen's Inequality Liao, J. G. ; Berg, Arthur This paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate result in spite of its simple form. chucklefish spellbound gameWebbSharpening Jensen's Inequality J. Liao, Arthur Berg Mathematics The American Statistician 2024 Abstract This article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides… Expand 50 PDF View 1 excerpt, references background desk and chair on saleWebbNow, 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 ... desk and chair ikea