Several Hermite-Hadamard Typ e Inequalities for Harmonically Convex Functions in the Second Sense with Applications

In this paper, we first introduce the concept“harmonically convex func-tions”in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.     

Fejer and Hermite-Hadamard type inequalities for superquadratic functions

In this paper we use basic properties of superquadratic functions to obtain new inequalities including Fejer's type and Hermite-Hadamard type inequalities. For superquadratic functions which are also convex, we get refinements of known results.     

On new inequalities of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex with applications

We establish some new inequalities of Hermite-Hadamard type for functions whose third derivatives absolute values are quasi-convex. Applications to special means have also been presented.     

多元凸函数的性质及其Hermite-Hadamard不等式

在多元凸函数的定义基础上,论述了多元凸函数的几种判定方法和一些性质,并证明了特殊区域上的Hermite-Hadamard不等式.     

涉及Gram行列式的一类不等式及应用

本文建立了涉及Gram行列式式的一类不等式。作为其应用，给出了关于垂足单形的一类不等式，导出了Hadamard不等式。     

The Hermite-Hadamard inequality in Beckenbach's setting

The classical Hermite-Hadamard inequality gives a lower and an upper estimations for the integral average of convex functions defined on compact intervals, involving the midpoint and the endpoints of the domain. The aim of the present paper is to extend this inequality and to give analogous results when the convexity notion is induced by Beckenbach families. The key tool of the investigations is based on some general support theorems that are obtained via the pure geometric properties of Beckenbach families and can be considered as generalizations of classical support and chord properties of ordinary convex functions. The Markov-Krein-type representation of Beckenbach families is also investigated.     

Multidimensional Hermite-Hadamard inequalities and the convex order

The problem of establishing inequalities of the Hermite-Hadamard type for convex functions on n-dimensional convex bodies translates into the problem of finding appropriate majorants of the involved random vector for the usual convex order. We present two results of partial generality which unify and extend the most part of the multidimensional Hermite-Hadamard inequalities existing in the literature, at the same time that lead to new specific results. The first one fairly applies to the most familiar kinds of polytopes. The second one applies to symmetric random vectors taking values in a closed ball for a given (but arbitrary) norm on Rn. Related questions, such as estimates of approximation and extensions to signed measures, also are briefly discussed.     

Some quantum estimates of Hermite-Hadamard inequalities for convex functions

In this study, based on a new quantum integral identity, we establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.     

A general multidimensional Hermite-Hadamard type inequality

Using a stochastic approach, we establish a multidimensional version of the classical Hermite-Hadamard inequalities which holds for convex functions on general convex bodies. The result is closely related to the Dirichlet problem.     

与GA-凸函数有关的两个函数

引入两个与GA-凸函数有关的函数,研究了它们的凸性、单调性及相互关系,获得了已有文献关于GA-凸函数的Hadamard型不等式的加细,也得到一些新的不等式.     

关于区间Katugampola分数阶积分的若干Hermite-Hadamard型不等式

主要引入了区间值函数Katugampola分数阶积分的概念.利用区间分析及区间凸函数理论,得到了区间Katugampola分数阶积分Hermite-Hadamard型不等式.     

New inequalities of Hermite-Hadamard type via s-convex functions in the second sense with applications

In this paper, we establish some new inequalities of Hermite-Hadamard type whose derivatives in absolute value are s-convex in the second sense. Finally some applications to special means of positive real numbers are given.     

Generalized Transportation-Cost Inequalities and Applications

For μ: = e ^V(x)dx a probability measure on a complete connected Riemannian manifold, we establish a correspondence between the Entropy-Information inequality and the transportation-cost inequality for μ(f ²) = 1, where Φ and Ψ are increasing functions. Moreover, under the curvature–dimension condition, a Sobolev type HWI (entropy-cost-information) inequality is established. As applications, explicit estimates are obtained for the Sobolev constant and the diameter of a compact manifold, which either extend or improve some corresponding known results. Supported in part by NNSFC(10721091) and the 973-project in China.     

三阶可微函数的若干不等式

通过建立与Bullen不等式有关的积分恒等式,利用Halder不等式、Grüss不等式、Chebychev不等式,给出三阶可微函数的一些不等式.     

泛函不等式及其应用

本文介绍有关泛函不等式及谱理论与马氏过程研究的若干新进展，我们首先简要回顾了两个著名不等式，即Poincare不等式与对数不等式，然后分别使用泛函不等式研究本征谱、马氏半群的收敛速度和运费不等式．     

一类新的Radon型不等式及其应用

给出一类新的R adon型不等式,它们在代数不等式研究中有着广泛的应用,利用它们可直接得到一大批新的分式型不等式,也可运用它们证明或推广许多不等式.     

涉及两个n维单形的四类不等式

给出了涉及两个n维单形的棱长、体积与外接球半径的四类不等式,从而推广和改进了相关文献的结果.     

多值单调映象的Browder-Hartman-Stampacchia型变分不等式

在Ｂａｎａｃｈ空间中,证明了多值单调映象的Ｂｒｏｗｄｅｒ－Ｈａｒｔｍａｎ－Ｓｔａｍｐａｃｃｈｉａ型变分不等式解的存在性定理,统一并推广了「４,５,６,９」中的主要结果。     

一组凹凸性不等式及其应用

基于函数凹凸性的定义和性质,推导了一组新的不等式,进而将其推广到n项形式,并给出了它们在求和式数列极限中的应用.     

Heisenberg型群上一类精确Hardy型不等式和Hardy-Sobolev型不等式及应用(英文)

本文在Heisenberg型群上建立了一类精确的Hardy型不等式。采用的技巧是逼近及正则化的方法。进一步利用这个结果,本文建立了一类精确的Hardy-Sobolev型不等式。这两个结果包括了已有的相关结果。作为应用,讨论了一类具有Hardy位势的非线性算子的正定性与下无界性。