Refining jensen's inequality

Author: bjqu

August undefined, 2024

WebJensen's inequality induces different forms of functionals which enables refinements for many classic inequalites. Several refinements of Jensen's inequalities were given. In this … WebUsing Jensen's inequality for convex functions and the second inequality in ( 6.26) we have (6.32) provided that (6.33) hold for every x ∈ [ a, b ]. The second condition in ( 6.33) is obviously satisfied. On the other hand, the increasing convex function ϕ with ϕ (0) = 0 is starshaped, thus ϕ ( ax) ≤ a ϕ ( x) holds for 0 < a ≤ 1.

Mathematics Free Full-Text A Refined Jensen Inequality …

WebJensen’s inequality states that if ϕ : [0,∞) → R is convex then (1.1) ϕ Z f dµ ≤ ϕ(f(s))dµ(s) for all probability measures µ and all non-negative, µ-integrable functions f. If ϕ is concave the … shane whitla lurgan

CiteSeerX — Refining Jensen’s inequality

WebA refinement of Jensen’s inequality is presented. An extra term makes the in-equality tighter when the convex function is “superquadratic, ” a strong convexity-type con-dition … WebEnter the email address you signed up with and we'll email you a reset link. Web1. sep 2015 · In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of time-delay systems. shane whitlock

Refining Jensen

Web18. dec 2024 · Jensen’s inequality has pertinence in every subject of biomathematics that consists of nonlinear processes, and this inequality gives a dynamic mechanism for … WebWe give refinement of Jensen’s type inequalities given by Bakula and Pečarić (2006) for the co-ordinate convex function. Also we establish improvement of Jensen’s inequality for … shane whitla facebookhttp://oam.ele-math.com/16-03/Refining-and-reversing-Jensen-s-inequality shane whitlow arrested

"Web1. 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 " - Refining jensen's inequality

Refining jensen's inequality

GENERALIZATION AND REFINEMENTS OF JENSEN INEQUALITY

Web6. jan 2024 · The principal aim of this research work is to establish refinements of the integral Jensen's inequality. For the intended refinements, we mainly use the notion … Web1. 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) …

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WebJensen's formula is a consequence of the more general Poisson–Jensen formula, which in turn follows from Jensen's formula by applying a Möbius transformation to z. It was … http://files.ele-math.com/abstracts/oam-16-03-abs.pdf

Web13. jan 2024 · Viewed 134 times. 0. According to wikipedia: Jensen's inequality is. f ( t x 1 + ( 1 − t) x 2) ≤ t f ( x 1) + ( 1 − t) f ( x 2). With this, I can easily prove Inequality of arithmetic and geometric means, in other words to prove that: x 1 + x 2 + ⋯ + x n n ≥ x 1 ⋅ x 2 ⋯ x n n, 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 …

WebRefining and reversing Jensen's inequality. Purchase this article; Recommend this article; DOI. DOI name: Click to select; Find all available articles from these authors. ... Primary; … Web14. nov 2024 · In this paper we deal with functions related to generalized convexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend …

WebJensen's inequality is just a mathematical way of describing that the convex function always lies below the secant line joining them for any two points. Background Extensions This inequality can be extended to many other useful inequalities as well. Generalization

WebJameson GJO, Abramovich S, Sinnamon G. Refining Jensen's inequality. Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie . 2004 Dec 1;47 … shane whitlow chargesWebDragomir, Sever S ORCID: 0000-0003-2902-6805 (2024) Refining Jensen's Integral Inequality for Divisions of Measurable Space. Journal of Mathematical Extension, 12 (2). pp. 87-106. … shane whitmanWebA 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 … shane whitleyWebRefining and reversing Jensen's inequality. Operators and Matrices. Hamid Reza Moradi. Download Download PDF. Full PDF Package Download Full PDF Package. This Paper. A … shane whitlow missingWebREFINING JENSEN™S INTEGRAL INEQUALITY FOR DIVISIONS OF MEASURABLE SPACE S. S. DRAGOMIR1;2 Abstract. In this paper we establish a re–nement and some reverses for … shane whitlow virginia beachWeb24. 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 … shane whitlow instagramWebJensen's inequality is an inequality involving convexity of a function. We first make the following definitions: A function is convex on an interval \(I\) if the segment between any … shane whitney