Webb琴生不等式 （英語： Jensen's inequality ，台湾稱作 簡森不等式 [1] ），或稱 延森不等式 ，以 丹麥 數學家 約翰·延森 命名。 它給出 積分 的 凸函數 值和凸函數的積分值間的關係，在此不等式最簡單形式中，闡明了對一平均做凸函數轉換，會小於等於先做凸函數轉換再平均。 若將簡森不等式應用在二點上，就回到了 凸函數 的基本性質：过一个凸函数上任意 … 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.
On a Lower Bound for the Jensen Inequality SIAM Journal on ...
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 … 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 Webb10 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 … simpsons of barham court beora
The Weighted Arithmetic Mean–Geometric Mean Inequality is …
WebbJensen’s inequality is a fundamental inequality in mathematics anditunderliesmanyimportantstatisticalproofsandconcepts. … Webb25 maj 2024 · The proof of Proposition 3.1 is based on Jensen’s inequality, but the reduction to constants is not obtained by applying Jensen’s inequality to show that … simpsons of barham court beora reserve 2019