Sharpening jensen's inequality

Author: pudx

August undefined, 2024

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]. Webb3 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 …

[1707.08644] Sharpening Jensen

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 … WebbSharpening 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. fitts stair parts online

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, … 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 … 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 … fitts seafood reviews

The Australian Journal of Mathematical Analysis and Applications …

Webb21 juli 2024 · And I carefully reviewed proof process of Jensen's Inequality and found Why "Jensen's inequality Do Not hold in general finite measure space". I write this thought down for anyone who has the same confusion. In the original Proof: Proof: WebbSharpening 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 fitts seafood marketWebbFurther sharpening of Jensen's inequality Sang Kyu Lee a Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA View further author … fitts seafood salem or

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Sharpening jensen's inequality

Inequalities for $$L^p$$ L p -Norms that Sharpen the Triangle ...

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 ... 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 …

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WebbJensen's inequality is an inequality involving convexity of a function. We first make the following definitions: A function is convex on an interval I I if the segment between any two points taken on its graph ( ( in I) I) lies above the graph. An example of a convex function is f (x)=x^2 f (x) = x2. A function is concave on an interval 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.

WebbIn 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. 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 …

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 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

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

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. can i get tbs on netflixWebb10 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 … fitts stages of learningWebb10 dec. 2024 · The Jensen inequality is one of the most famous and most important inequalities in math- ematical analysis. In [ 2 ], some estimates about the sharpness of … fitts sign companyWebbJensen’s inequality is a fundamental inequality in mathematics anditunderliesmanyimportantstatisticalproofsandconcepts. … fitts stairWebb18 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 … can i get tbs over the airWebb4 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 … can i get tbs on huluWebbThe 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. can i get tax free childcare