几个新的不等式及其应用

本文给出几个新的不等式,并运用其解决有关数列和式的不等式证明题.1几个新的不等式定理1设b>0,a>max|b,b~(1/2)|,则对(?)_n∈     

反向基本不等式及应用

运用导数方法,对两个正数的基本不等式中的权数作了分析研究,给出了基本不等式的三个反向不等式;运用反向不等式,通过选取适当的权数,给出了指数平均的反向不等式,同时给出了涉及A,G,L,E的几个新的不等式.     

算子Dunkl-Williams型不等式

在于讨论和经典Dunkl-Williams型不等式相类似的算子不等式,得到了几个算子Dunkl-Williams型不等式,并将其与现有的不等式进行了比较,结果表明,所得的结果是前期结果的推广和改进.     

涉及两个单形的几何不等式及应用

建立了涉及两个n维单形的几个不等式,推广了一些重要几何不等式.     

阿达玛不等式在证明初等不等式中的应用

通过运用阿达玛不等式,给出了几个初等不等式的证明.     

不等式的性质和证明

本单元的主要内容是：不等式的概念和性质、几个重要的不等式以及不等式的证明，它们之间的关系可用网络图表示如下：     

一类新的多重积分不等式与等式的构造及其应用

首先引入二重积分的分部积分公式和柯西-施瓦茨不等式,然后利用它们构造一类新的二重积分的不等式与等式,并推广到三重积分,得到几个相关结论．最后给出几个具体应用实例,以验证其实用性．     

一道数学竞赛题的联想

用级数方法证明了一个三角不等式,同时还得到了几个新的三角不等式.     

关联单形和一点的一类几何不等式

本文建立联系单形和一动点的几个新颖不等式,并提出几个有待进一步讨论的猜想.     

关于有界函数的一个不等式

在三角函数中y=sinx,y=cosx均为有界函数．我们也经常看到有关三角不等式涉及几个三角函数值的积与和的不等式的证明题．为此笔者对有界函数作了研究,发现从有界函数的定义出发,推导出该有界函数的任意几个函数值的和与积之间的一个不等式．     

Operator-norm inequalities and interpolated trace inequalities

In this article, we investigate some operator-norm inequalities related to some conjectures posed by Hayajneh and Kittaneh that are related to questions of Bourin regarding a special type of inequalities referred to as subadditivity inequalities. While some inequalities are meant to answer these conjectures, other inequalities present reverse-type inequalities for these conjectures. Then, we present some new trace inequalities related to Heinz means inequality and use these inequalities to prove some variants of the aforementioned conjectures.     

Functional inequalities for the Wright functions

In this paper, our aim is to show some mean value inequalities for the Wright function, such as Turán-type inequalities, Lazarevi?-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for sections of series of Wright functions, the result is also closely connected with Turán-type inequalities. In the end of the paper, we present some other inequalities for the Wright function.     

Merit functions for general variational inequalities

In this paper, we consider some classes of merit functions for general variational inequalities. Using these functions, we obtain error bounds for the solution of general variational inequalities under some mild conditions. Since the general variational inequalities include variational inequalities, quasivariational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. In this respect, results obtained in this paper represent a refinement of previously known results for classical variational inequalities.     

Some logarithmic Minkowski inequalities for nonsymmetric convex bodies

We prove some analogs inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies. As applications of one of those inequalities, the p-affine isoperimetric inequality and some other inequalities are obtained.     

Projection algorithms for the system of mixed variational inequalities in Banach spaces

In this paper, the system of mixed variational inequalities is introduced and considered in Banach spaces, which includes some known systems of variational inequalities and the classical variational inequalities as special cases. Using the projection operator technique, we suggest some iterative algorithms for solving the system of mixed variational inequalities and prove the convergence of the proposed iterative methods under suitable conditions. Our theorems generalize some known results shown recently.     

Gap inequalities for non-convex mixed-integer quadratic programs

Laurent and Poljak introduced a very general class of valid linear inequalities, called gap inequalities, for the max-cut problem. We show that an analogous class of inequalities can be defined for general non-convex mixed-integer quadratic programs. These inequalities dominate some inequalities arising from a natural semidefinite relaxation.     

Some singular value and unitarily invariant norm inequalities for Hilbert space operators

In this paper, we prove some singular value inequalities for sum and product of operators. Also, we obtain several generalizations of recent inequalities. Moreover, as applications we establish some unitarily invariant norm and trace inequalities for operators which provide refinements of previous results.     

Schur-Convex Functions and Isoperimetric Inequalities

In this paper, we establish some analytic inequalities for Schur-convex functions that are made of solutions of a second order nonlinear differential equation. We apply these analytic inequalities to obtain some geometric inequalities.

     

Inequalities for convex functions via Stieltjes integral

We present a method of proving inequalities for convex functions with use of Stieltjes integral. First, we show how some well-known inequalities can be obtained, and then we show how new inequalities and stronger versions of some existing results can be obtained.