Sharpening jensen's inequality
WebbWe obtain a scalar inequality, converse to the Jensen inequality. We also derive an op-erator converse to the Jensen inequality. As special cases, we obtain inequalities, similar to the Kantorovich one as well as some operator generalizations of them. Using some exterior algebra, we prove a generalization of the Sylvester determinant theorem. 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.
Sharpening jensen's inequality
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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 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 …
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 WebbThis 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 …
WebbJensen's Inequality Continuous Form It Application Interpolation Result We give a refinement of the converse Hölder inequality for functionals using an interpolation result for Jensen’s inequality. Additionally, we obtain similar improvements of the converse of the Beckenbach inequality. Webb18 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 …
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 …
Webb19 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 … how are orchids adapted to the rainforestWebb12 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. how are orbeez made youtubeWebb3 juli 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 … how many mgs of magnesium should i take a dayWebbSharpeningJensen’s Inequality J. G. Liao and Arthur Berg Division of Biostatistics and Bioinformatics Penn State University College of Medicine October 26, 2024 Abstract This … how are orchestras organizedWebbIn 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 how are orcs born in lord of the ringsWebbFurther sharpening of Jensen's inequality Sang Kyu Lee a Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA View further author … how are ordinary dividends taxed in 2020WebbIn this paper we introduce a new mapping connected with the classical inequality due to Jensen and point out its main properties. Some applications related to well-known inequalities are also established. how many mgs of thc