Sharpening jensen's inequality

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August undefined, 2024

WebbIn this article, we consider the generalized forms of the Jensen's inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen's and McShane's inequalities connected to certain functions from the linear space, generalize the Jessen's and McShane's inequalities pertaining n certain functions. 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 …

Sharpening 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, … WebbJensen’s inequality is covered in all major statistical textbooks such as Casella and Berger ( 2002, Section 4.7) and Wasserman ( 2013, Section 4.2) as a basic mathematical tool … dewalt cordless pressure cleaner

A Reverse Jensen Inequality Result with Application to Mutual ...

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 … 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. WebbJensen’s inequality is covered in all major statistical textbooks such as Casella and Berger ( 2002, Section 4.7) and Wasserman ( 2013, Section 4.2) as a basic mathematical tool for statistics. Let X be a random variable with finite expectation and let φ(x) be a convex function. Jensen’s inequality (Jensen, 1906) establishes: E[φ(X)]− φ(E[X]) ≥ 0. dewalt cordless press tool

Jensen

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 WebbJensen’s inequality is a fundamental inequality in mathematics anditunderliesmanyimportantstatisticalproofsandconcepts. … dewalt cordless pressure washer home depotWebbReduce inequality within and among countries - United Nations Sustainable Development. Home. About. Goals. Take Action. Partnerships. News and Media. Learn more. UN 2024 Water Conference. church meeting room crossword clue 6

"WebbIn this paper we shall show that sharpening Holder’s Inequality can be¨ generalized to sharpen Jensen’s inequality for concave and convex func-tions 1, 4 .wx We shall also sharpen a majorization theorem for concave functions and two sequences or functions when only one of them is monotonic 6 . . wx 2. SHARPENING JENSEN’S INEQUALITY " - Sharpening jensen's inequality

Sharpening jensen's inequality

About the sharpness of the Jensen inequality Semantic Scholar

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 … WebbDragomir, Sever S ORCID: 0000-0003-2902-6805 (2024) Refining Jensen's Integral Inequality for Partition of Weights. Libertas Mathematica (new series), 37 (1). 25 - 44. ISSN 0278-5307

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WebbSharpening Jensen's Inequality Published in: The American Statistician, June 2024 DOI: 10.1080/00031305.2024.1419145: Authors: J. G. Liao, Arthur Berg View on publisher site Alert me about new mentions. Twitter Demographics. The data shown below were collected from the profiles of 4 tweeters who shared this research output. Webb4 sep. 2024 · In recent years, many researchers have been interested in studying the mathematical equivalence among some famous analytical inequalities, such as the Cauchy–Schwarz inequality, the Bernoulli inequality, the Wielandt inequality, and the Minkowski inequality; see [7,8,9,10,11,12,13] for details.Additionally, these studies note …

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 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.

Webb26 juli 2024 · Sharpening Jensen's Inequality J. G. Liao, Arthur Berg This paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple … Webb10 dec. 2024 · The 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 considering the case of the real Stieltjes measure, not necessarily positive. Finally, some applications involving various types of f-divergences and …

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].

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 … church meeting room crossword clueWebbHowever, applying Jensen on log-sums in Ie and £(XIE» is not as straightforward. Some terms in these expressions involve negative log-sums and so Jensen is actually solving for an upper bound on those terms. If we want overall lower and upper bounds on Ie and £(XIE», we need to compute reverse-Jensen bounds. 5 Reverse-Jensen Bounds church meeting room rentalWebb25 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 … dewalt cordless power washersWebb18 dec. 2024 · The prime purpose of this paper is to provide a refinement of Jensen’s inequality in connection with a positive finite sequence. We deal with the refinement for particular cases and point out the relation between the new result with earlier results of Jensen’s inequality. As results, we obtain refinements of the … dewalt cordless pump for waterWebb6 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 … church meeting roomsWebbRefinements 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 dewalt cordless productsWebb19 nov. 2024 · Jensen's inequality的背景是独特的形象化的。但凡看的的懂图像的人，都能从函数图像上直观的感受到这个不等式是自然成立的，而这正是优秀的数学工作的特点——简洁而不平凡。通过它还可证明基本不等式，只需构造简单的函数关系即可，非常简单明了。除了居高临下看过往，它还可高瞻远瞩建桥梁。 Young's inequality也可 … church meeting room crossword clue 6 letters