Sharpening jensen's inequality
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, … http://personal.psu.edu/asb17/papers2/Liao,Berg_2024_The-American-Statistician.pdf
Sharpening jensen's inequality
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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. 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 ...
http://ele-math.com/static/pdf/books/17689-MIA19.pdf 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 …
Webb12 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. 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
Webbvide 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.
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]. claiming age relaxation upsc meansWebbelifesciences.org downers grove brazilian steakhouseIn 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 downers grove buy buy babyWebb3 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 … claiming aged pension australiaWebbRefinements 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 downers grove crime blotterWebb10 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 … downers grove chimney sweepWebb3 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 … downers grove christmas lights