Refining jensen's inequality
WebA refinement of Jensen’s inequality is presented. An extra term makes the inequality tighter when the convex function is “superquadratic”, a strong convexity-type condition is … Web24. okt 2006 · In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some …
Refining jensen's inequality
Did you know?
http://oam.ele-math.com/16-03/Refining-and-reversing-Jensen-s-inequality Web1. sep 2015 · Remark 5. In most recent work [], by employing the Bessel inequality, an elegant integral inequality, namely Bessel–Legendre (B–L) inequality, was derived based …
http://files.ele-math.com/abstracts/mia-11-07-abs.pdf 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 in 1889. Given its generality, the inequality appears in many forms depending on t…
Web31. dec 2024 · In [], Horváth developed a general method to refine the discrete Jensen’s inequality in the convex and mid-convex cases.The main part of the inequalities in … WebProbability & Statistics Solved Examples of Jensen's Inequality Dr. Harish Garg 27.4K subscribers Subscribe 858 views 4 months ago This lecture will describe the examples of …
Web12. 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.
Web1. jan 2016 · The Lebesgue integral version of the Jensen inequality is given below: Theorem 1.1. Let (Ω, Λ, μ) be a measure space with 0 < μ (Ω) < ∞ and let ϕ : I → ℝ be a … bapen bmi pdfWebRefining and reversing Jensen's inequality. Operators and Matrices. Hamid Reza Moradi. Download Download PDF. Full PDF Package Download Full PDF Package. This Paper. A … bapen bifaWeb1. apr 2024 · This article is published in Octogon Mathematical Magazine archive.The article was published on 2002-04-01 and is currently open access. It has received 16 citation(s) … bapen buried bumperWebObtained results are used to refine monotonicity properties for power means of Mercer’s type, and a comparision theorem for quasi-arithmetic means of Mercer’s type for … bapen dementiaWebJensen'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 bapen must muacWeb“convexity and Jensen’s inequality can be made the foundation of a theory of inequalities” The subject is quoted from Boyd, Stephen P. and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004. Can anybody explain what this means? convex-optimization jensen-inequality beroal 2,392 asked Mar 1 at 17:08 2 votes 0 answers bapen meaningWeb1. mar 2024 · Jensen's inequality states that for a convex function f: I → R and x1,..., xn ∈ I, we have 1 n n ∑ i = 1f(xi) ≥ f(1 n n ∑ i = 1xi) But in order to use this inequality, you have to choose the right function. Take for example this problem x1,..., xn are positive reals such that n ∑ i = 1 1 1 + xi = 1 Show that n ∏ i = 1xi ≥ (n − 1)n bapen muac