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#11. A new refinement of Jensen's inequality with applications in ...

Jensen's inequality probably plays a crucial role in the theory of mathematical inequalities. It is applied widely in mathematics, statistics, ...

#12. New refinement of the Jensen inequality associated to certain ...

This article proposes a new refinement of the celebrated Jensen inequality. Some refinements have been obtained for quasi-arithmetic means, ...

#13. A FURTHER IMPROVEMENT OF JENSEN'S INEQUALITY

A FURTHER IMPROVEMENT OF JENSEN'S INEQUALITY. SEVER SILVESTRU DRAGOMIR. 1. Introduction. In the Theory of Inequalities, the famous Jensen's discrete ...

#14. Jensen's inequality | Proof, examples, solved exercises

Jensens's inequality is a probabilistic inequality that concerns the expected value of convex and concave transformations of a random variable.

#15. A Visual Explanation of Jensen's Inequality - jstor

of Jensen's Inequality. Tristan Needham. "This theorem is so fundamental that we propose to give a number of proofs, of varying degrees of simplicity and ...

#16. Jensen's inequality in geodesic spaces with lower bounded ...

Jensen's inequality in geodesic spaces with lower bounded curvature. Authors:Quentin Paris · Download PDF. Abstract: Let (M,d) be a separable ...

#17. Jensen's Inequality - Art of Problem Solving

Jensen's Inequality is an inequality discovered by Danish mathematician Johan Jensen in 1906. Contents. [hide]. 1 Inequality; 2 Proof; 3 ...

#18. Recent Research on Jensen's Inequality for Oparators

2.1. Jensen's inequality with operator convexity. Firstly, we give a general formulation of Jensen's operator inequality for a unital field of positive linear ...

#19. Jensen's inequality for nonconvex functions - CORE

Jensen's inequality is 100 years old, e.g., [1, 2, 3] . It says that the value of a convex function at a point, which is a convex combination of finitely ...

#20. 1.1 Jensen's Inequality - CUHK Mathematics

It is strictly convex if strict inequality holds in this condition whenever x = y and λ ∈ (0,1). Jensen's Inequality. Let f be a convex function on the ...

#21. On the Jensen's inequality and its variants - AIMS Press

The main purpose of this paper is to discuss operator Jensen inequality for convex functions, without appealing to operator convexity.

#22. On An Upper Bound For Jensen's Inequality - emis.de

For instance, we determine a new converse for the generalized A − G inequality. Key words and phrases: Jensen's discrete inequality, global bounds, generalized ...

#23. Chapter 2 Inequalities involving expectations - Bookdown

Jensen's Inequality is a statement about the relative size of the expectation of a function compared with the function over that expectation (with respect ...

#24. Convexity and Jensen's Inequality - Andrew B. Nobel

If f is strictly concave and X is not constant then the inequality is strict. Note: Definition of convexity is a special case of (2) for random vector X ∈ C.

#25. Jensen's inequality predicts effects of environmental ... - PubMed

Jensen's inequality is a mathematical proof that is seldom mentioned in the ecological literature but which provides a powerful tool f …

#26. A Gentle Introduction to Jensen's Inequality - Machine ...

Jensen's Inequality suggests that the mean of the payoffs will always be larger than or equal to the payoff of the mean outcome. Recall that the ...

#27. Converses of the Jensen inequality derived from the Green ...

Jensen integral inequality has got much importance regarding their applications in different fields of mathematics.

#28. Jensen's Inequality | Part II: Inference & Limit Theorems - MIT ...

Jensen's inequality applies to the special case where g is a convex function. I'm going to define more precisely what it means to be convex shortly. But in ...

#29. Jensen Inequality

Jensen Inequality. Theorem 1. Let f be an integrable function defined on [a, b] and let φ be a continuous (this is not needed).

#30. Convex Functions and Jensen's Inequality - Berkeley Math

Convex Functions and Jensen's Inequality ... is concave. If you are familiar with derivatives then the following theorem about twice differentiable functions ...

#31. Jensen's Inequality for Operators and Löwner 's Theorem.

Hansen, Frank, and Pedersen, Gerd Kjaergard. "Jensen's Inequality for Operators and Löwner 's Theorem.." Mathematische Annalen 258 (1981): 229-242.

#32. Immortal Economists: Jensen's Inequality

Jensen's inequality studies convex functions and the relationship between their mean values. It is stated as follows: If X is a real-valued random variable ...

#33. Jensen's Inequality

Jensen's Inequality plays a central role in the derivation of the Expectation Maximization algorithm [1] and the proof of consistency of maximum ...

#34. A REFINEMENT OF JENSEN'S INEQUALITY WITH ...

A refinement of the discrete Jensen's inequality for convex functions defined on a convex subset in linear spaces is given. Application for f f -divergence ...

#35. Jensen's inequality - MyWeb

Theorem: If g is a convex function defined over an interval I , and X is a random variable with P ( X ∈ I ) = 1 and finite expectation, then g ...

#36. Jensen's Inequality and the Impact of Short-Term ... - PLOS

Jensen's Inequality and the Impact of Short-Term Environmental Variability on Long-Term Population Growth Rates. Evan J. Pickett,.

#37. Full article: Further sharpening of Jensen's inequality - Taylor ...

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.

#38. New refinement of the Jensen inequality associated to certain ...

Keywords: Jensen's inequality; Convex functions; Hölder inequality; Means; ... Jensen's inequality is one of the fundamental inequalities in mathematics and ...

#39. ON JENSEN'S INEQUALITY FOR g-EXPECTATION - World ...

Briand et al. gave a counterexample showing that given g, Jensen's inequality for g-expectation usually does not hold in general.

#40. Jensen's Inequality for Separately Convex Noncommutative ...

Abstract. Classically, Jensen's Inequality asserts that if $X$ is a compact convex set, and $f:K\to {\mathbb {R}}$ is a convex function, ...

#41. Convexity, and Jensen's inequality (Chapter 4) - Cambridge ...

Many important inequalities depend upon convexity. In this chapter, we shall establish Jensen's inequality, the most fundamental of these inequalities, ...

#42. On Reversing Jensen's Inequality - NeurIPS Proceedings

Authors. Tony Jebara, Alex Pentland. Abstract. Jensen's inequality is a powerful mathematical tool and one of the workhorses in statistical learning.

#43. On the use of Jensen's inequality for MIMO channel capacity ...

On the use of Jensen's inequality for MIMO channel capacity estimation. Abstract: We derive a universal upper bound on the MIMO channel capacity, ...

#44. Jensen's inequality for quasiconvex functions - American ...

Some inequalities of Jensen type and connected results are given for quasiconvex functions on convex sets in real linear spaces.

#45. Some companion inequalities to Jensen's inequality

Some companion inequalities to Jensen's inequality · DOI · Find all available articles from these authors · Find more articles with the same subject classes · Find ...

#46. A Converse of the Jensen Inequality for Convex Mappings of ...

In this paper we point out a converse result of the celebrated Jensen inequality for di erentiable convex mappings of several variables and ...

#47. Jensen Inequality of Bivariate Function in the G-Expectation ...

When expected utility function denotes the aversion and preference of risk, the Jensen's inequality of mathematical expectation takes an important role. Because ...

#48. On Reversing Jensen's Inequality

One simplification is to lower bound via Jensen's inequality or EM. The reverse upper bound is then derived. We show implementation and results of the bounds in ...

#49. Jensen's inequality formula | Bionic Turtle

In all generality Jensen's inequality says that for a convex (concave) function f, the expectation of the function of a random variable X ...

#50. Notes on sharpening Jensen's Inequality - HackMD

the function's curvature is high in the support of the random variable X X . If the function is linear, Jensen's inequality is in fact an equality.

#51. On a Lower Bound for the Jensen Inequality - SIAM epubs

Abstract. We present an improvement to the Jensen inequality for certain convex functions φ on (0 ∞). This implies finding a nonzero lower ...

#52. On Jensen's inequality for the power function of norm of ...

Jensen's inequality, the so-called king of inequalities [7], is actually a fundamental theoretical tool for convex analysis and derives many other important ...

#53. Jensen inequality - Oxford Reference

For a random variable, X, the inequality (given by Jensen in 1906) states that E[g(X)]≥g [E(X)], where E denotes expected value and g denotes any convex ...

#54. When Jensen's inequality is equality - Mathematics Stack ...

When Jensen's inequality is equality ... If X is a random variable and g is a convex function, then E(g(X))≥g(E(X)). Just out of curiosity, when do we have ...

#55. Variable ventilation and Jensen's inequality: citation corrections

This explanation is advanced in a paper by us and not cited ('Convexity, Jensen's inequality and benefits of noisy mechanical ventilation' ...

#56. Jensen's Inequality - Maths, HKUST

sin x on [0, π ]. The most important inequalities con-cerning these functions are the following. Jensen's Inequality. If f is convex on an interval I and.

#57. Multivariate Jensen's Inequality - Lei Mao

Jensen's inequality could be used for proving a lot of useful mathematical properties. Jensen's inequality for the univariate case is very ...

#58. A Double‐Weighted Refinement of Jensen's Inequality with ...

A Double‐Weighted Refinement of Jensen's Inequality with Applications. AIP Conference Proceedings 936, 700 (2007); https://doi.org/10.1063/ ...

#59. Jensen's inequality for conditional expectations - UiO

Jensen's inequality for conditional expectations. We start with a few general results on convex functions f : Rn → R. Theorem 1. Any convex function f : Rn ...

#60. Some Generalizations of Jensen's Inequality - Universal Wiser ...

In this article, we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where ...

#61. A weakened version of Davis-Choi-Jensen's inequality for ...

http://dx.doi.org/10.4067/S0716-09172017000100005 · A weakened version of Davis-Choi-Jensen's inequality for normalised positive linear maps · S. S. Dragomir.

#62. What is an intuitive explanation of Jensen's Inequality? - Quora

Jensen's inequality really just says that the inequality defining a convex function generalizes well to convex combinations of multiple things. It's a ...

#63. Convexity at a point and Jensen inequality - MathOverflow

Your generalization of Jensen's inequality follows immediately from the well-known fact that any probability distribution μ on R with a ...

#64. Jensen's inequality | Topic | Microsoft Academic

Definition. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to ...

#65. Operator Jensen's Inequality for Operator Superquadratic ...

How to cite: Alomari, M.W. Operator Jensen's Inequality for Operator Superquadratic Functions. Preprints 2019, 2019120206 (doi: ...

#66. Chapter 2, Lecture 4: Jensen's inequality - Math

Jensen's inequality —one of the most useful inequalities that ever inequalitied—is the result be- low: Theorem 1.1. For any λ1,λ2,...,λk ≥ 0 ...

#67. The Jensen's inequality and functional form of Jensen's ...

Authors. Yu Ming Chu - Department of Mathematics, Huzhou University, Huzhou, China. Imran Abbas Baloch - Abdus Salam School of Mathematical Sciences GC ...

#68. Jensen's Inequality - Interactive Mathematics Miscellany and ...

Jensen's Inequality : for a convex function f and a + b + ... + c = 1, f(ax + by + ... + cz) is not greater than af(x) + bf(y) + ... + cf(z)

#69. Convexity, Jensen's inequality, and benefits of noisy or ...

Life support with a mechanical ventilator is used to manage patients with a variety of lung diseases including acute respiratory distress syndrome (ARDS).

#70. Jensen's Inequality (Real Analysis) - ProofWiki

This proof is about Jensen's Inequality in the context of Real Analysis. For other uses, see Jensen's Inequality.

#71. Jensen's Inequality Predicts Effects of Environmental Variation

Jenson's inequality is a mathematical proof that is seldom mentioned in the ecological literature but which provides a powerful tool for predicting some ...

#72. Jensen's Inequality and majorization - NASA/ADS

... operator convex, monotone convex and arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered.

#73. About the Jensen inequality - Djalil CHAFAI

All is about the Jensen inequality, one of my favorite inequality, which connects convexity and probability in a rigid way.

#74. Application of Convex Functions and Jensen Inequality

Keywords: Convex function; Jensen inequality; Integral inequality; Application; Abstract. Functions are the important fundamental concepts in mathematics ...

#75. Jensen's inequality and its converses

Generalization of converses of Jensen's inequality. 3. Quasi-arithmetic means. Monotonicity. Difference and ratio type inequalities. 4. Power functions.

#76. Jensen's Inequality and the Success of Linear Prediction Pools

Jensen's Inequality and the Success of Linear Prediction Pools F Krüger. Download Read article. 509 KB, PDF. © Deutsche Bundesbank; Imprint · Freedom of ...

#77. Reciprocal Convexity to reverse the Jensen Inequality - B.log

Jensen's inequality is a powerful tool often used in mathematical derivations and analyses. It states that for a convex function f(x) and an ...

#78. What is Jensen's Inequality and What is its Role in Finance?

(Concave is the opposite, simply — f is convex.) Jensen's Inequality and convexity can be used to explain the relationship between randomness in stock prices ...

#79. The Variance Drain and Jensen's Inequality Robert A. Becker

A new form of the AM-GM Inequality follows and is is applied to financial returns. Both exact, and approximate relations between the arithmetic ...

#80. New Estimates for the Jensen Gap Using s-Convexity With ...

Several mathematical inequalities have been established for s-convex functions in particular [21–28], one of the most important being the Jensen ...

#81. Sharpening Jensen's Inequality - Penn State Pure

This article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable ...

#82. [PDF] Sharpening Jensen's Inequality | Semantic Scholar

Abstract This article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, ...

#83. Jensen's Inequality - GeoGebra

Jensen's Inequality. Author: Paul Walter. GeoGebra Applet Press Enter to start activity. New Resources. Open Middle Challenge: Parallel Lines and Related ...

#84. Revista Colombiana de Matemáticas - SciELO Colombia

Abstract A refinement and a new sharp reverse of Jensen's inequality for convex functions in terms of divided diferences is obtained. Applications for means, ...

#85. on the ubiquity, utility and continuing novelty of Jensen's ...

This basic property of nonlinear averaging – known as 'Jensen's inequality' or 'the ...

#86. Reducing the gap of Jensen's inequality by using Wirtinger ...

In order to illustrate the potential gain of employing this new inequality with respect to the Jensen's one, two applications on time-delay and ...

#87. Jensen's inequality - HandWiki

In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the ...

#88. Inequalities and Applications: Conference on Inequalities ...

There are many known inequalities for convex functions , but surely the most important of them is Jensen's inequality . In its integral form it is stated as ...

#89. Jensen's inequality - Academic Kids

In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the ...

#90. Jensen's inequality - BLOG

This is an illustrative explanation of Jensen's inequality applied to probability. Jensen's inequality. Remember that a convex function is a ...

#91. MathType on Twitter: "Jensen's #inequality generalizes the ...

Jensen's #inequality generalizes the fact that the secant line of a convex function lies above the graph of the function. It is important in #Probability ...

#92. MathType - Facebook

Jensen's Inequality explains how convex (e.g. x^2) and concave (e.g. log x) functions affect means #Analysis #MathType.

#93. Jensen's inequality: Cosmos — All that is, or was, or ever will be

Jensen's inequality. cosmos 4th November 2016 at 2:43pm ... (this is a nice case, one can imagine less intuitive cases, but the inequality is still true).

#94. Inequalities: A Journey into Linear Analysis - 第 24 頁 - Google 圖書結果

4.1 Convex sets and convex functions Many important inequalities depend upon convexity. In this chapter, we shall establish Jensen's inequality, ...

#95. A (perhaps naive) question about Jensen's inequality - Reddit

Jensen's inequality is a critical step to derive ELBO in variational inference. It seems to me that Jensen's inequality only applies when ...

#96. Martingale Methods in Financial Modelling - 第 28 頁 - Google 圖書結果

Before continuing our analysis of American options in an arbitrage-free oneperiod model, let us recall Jensen's inequality. We consider here only a special ...

#97. ASYMPTOTICS II MAXIMUM LIKELIHOOD ESTIMATION

Jensen's Inequality : Suppose X is a random variable with E(X) = µ, ... This inequality will be used to get the consistency of the ML estimator.

#98. Modern Discrete Mathematics and Analysis: With Applications ...

Dragomir, S.S.: Some refinements of Ky Fan's inequality. J. Math. Anal. Appl. 163(2), 317–321 (1992) Dragomir, S.S.: Some refinements of Jensen's inequality ...