共查询到20条相似文献,搜索用时 156 毫秒
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利用Cauchy-Schwarz不等式、Young不等式和HG凸函数定义,得到几个HG凸函数的Hermite-Hadamard型不等式. 相似文献
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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. 相似文献
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基于m-凸函数提出了一类称为模糊值m-凸函数的新概念.首先,研究了模糊值m-凸函数的若干基本性质;其次,给出了模糊值m-凸函数的共轭函数的概念,并给出了模糊值m-凸函数在一定的条件下的共轭函数是模糊值m-凸函数等相关性质;最后,讨论了两个模糊值m-凸函数的共轭函数与其下卷积的共轭函数之间的相互关系. 相似文献
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Zlatko PAVIC 《数学研究及应用》2016,36(1):51-60
The article deals with generalizations of the inequalities for convex functions on the triangle. The Jensen and the Hermite-Hadamard inequality are included in the study. Considering a convex function on the triangle, we obtain a generalization of the Jensen-Mercer inequality, and a refinement of the Hermite-Hadamard inequality. 相似文献
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Dah-Yan Hwang 《Applied mathematics and computation》2011,217(23):9598-9605
Several inequalities for differentiable convex, wright-convex and quasi-convex mapping are obtained respectively that are connected with the celebrated Hermite-Hadamard integral inequality. Also, some error estimates for weighted Trapezoid formula and higher moments of random variables are given. 相似文献
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An interesting property of the midpoint rule and the trapezoidal rule, which is expressed by the so-called Hermite-Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite-Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. In particular, for simplices of arbitrary dimension, we present two families of integration formulae which both contain a multivariate analogue of the midpoint rule and the trapezoidal rule as boundary cases. The first family also includes a multivariate analogue of a Maclaurin formula and of the two-point Gaussian quadrature formula; the second family includes a multivariate analogue of a formula by P.C. Hammer and of Simpson's rule. In both families, we trace out those formulae which satisfy a Hermite-Hadamard inequality. As an immediate consequence of the latter, we obtain sharp error estimates for twice continuously differentiable functions.
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In this paper, we give a weighted form of the Hermite-Hadamard inequalities. Some applications of them are also derived. The results presented here would provide extensions of those given in earlier works. Finally we pose two interesting problems. 相似文献
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Shahid Khan Muhammad Adil Khan Yu-Ming Chu 《Mathematical Methods in the Applied Sciences》2020,43(5):2577-2587
Jensen integral inequality has got much importance regarding their applications in different fields of mathematics. In this paper, two converses of Jensen integral inequality for convex function are obtained. The results are applied to establish converses of Hölder and Hermite-Hadamard inequalities as well. At the end, some useful applications in information theory of the obtained results are given. The idea used in this paper may inculcate further research. 相似文献
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Let $I$ be an open interval of $\mathbb{R}$ and $f: I\to \mathbb{R}$. It is well-known that $f$ is convex in $I$ if and only if, for all $x,y\in I$ with $x相似文献
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We establish various inequalities for n-times differentiable
mappings that are connected with illustrious Hermite-Hadamard
integral inequality for mapping whose absolute values of
derivatives are $\left( {\alpha ,m} \right)$-preinvex function.
The new integral inequalities are then applied to some special
means 相似文献
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Sever S. Dragomir 《Applications of Mathematics》2004,49(2):123-140
New properties for some sequences of functions defined by multiple integrals associated with the Hermite-Hadamard integral inequality for convex functions and some applications are given. 相似文献
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Mihály Bessenyei 《Journal of Mathematical Analysis and Applications》2010,364(2):366-383
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. 相似文献