关于凸函数的一般平均不等式

本文提出并证明了凸函数的最一般的平均不等式 ,是凸函数的幂平均、双参数平均不等式的进一步推广     

凸函数的双参数平均不等式

凸函数的双参数平均不等式孙明保（岳阳大学基础课部，湖南４１４０００）关键词双参数平均，不等式．分类号ＡＭＳ（１９９１）２６Ｄ／ＣＣＬＯ１７４．１３设ｆ（ｘ）在［ａ，ｂ］上可积且下界为正，则ｆ（ｘ）在［ａ，ｂ］上的双参数平均定义为Ｍｐ，ｑ（ｆ）＝∫ｂ...     

关于凸函数的双参数平均不等式

本文利用二重积分证明了凸函数的双参数平均不等式,并给出了它的几个推论从而推广和加强了文[3]的定理。     

双参数拓广平均单调性的一个简单证明

本文利用切比雪夫积分不等式和微分中值定理,对所谓的双参数拓广平均的单调递增性给出一种简单的证明。还简要地介绍了平均值理论的最新进展和研究结果。     

一个含多参数且-4齐次核的Hilbert型积分不等式

以Hilbert不等式为代表的双线型不等式是分析学的重要不等式.应用权函数方法,引入多个参数,建立了一个新的具有最佳常数因子的-4齐次核的双线型不等式.作为应用,导出其等价形式及一些特殊结果.     

Rado不等式的多参数推广及应用

通过引入加权幂平均以及参数α、β、μ建立一个新的R ado型不等式,由于所得不等式中含多个参数,因此是一个非常广泛的结果,可以通过对参数的适当取值得到一些已知结果的改进(如著名的Popov iciu不等式的改进),同时也可获得许多新的不等式.最后,我们应用所得结果给出加权幂平均不等式以及加权平均不等式的加细形式.     

关于双参数广义三角函数与双曲函数的不等式

利用经典的Bernoulli不等式,通过初等解析方法与不等式理论建立了带双参数广义三角函数与双曲函数的Gr¨unbaum型不等式;另外,还得到了推广超几何级数3F2的两个双边不等式.     

Hilbert格上双参数广义变分不等式问题解映射的保序性

本文不假设所考虑集值映射的连续性和单调性,在可分Hilbert格上研究广义变分不等式问题的可解性,并将已有结果中单参数广义变分不等式问题解映射的保序性推广到双参数广义变分不等式问题。     

三类三角函数的最值

三类三角函数的最值浙江普陀中学徐和郁文［１］、［２］相继讨论了两类三角函数的最小值，所用的方法都是巧妙地构造平均不等式．本文将通过构造带参数的平均不等式，来讨论另三类三角函数的最值．１求函数且的最小值．解引入参数λ、μ＞０，并构造如下平均不等式：（１...     

基于双参数罚函数求解约束优化问题的一个新算法

对于含约束不等式的最优化问题给出了一种双参数罚函数形式,在文[7]的拟牛顿算法的基础上提出了一个同时改变双参数罚函数的新算法,研究了它的收敛性,数值实验表明了该算法是有效的.     

How Big Are the Increments of a Two-Parameter Gaussian Process?

Some limit theorems on the increments of a two-parameter Gaussian process are obtained via estimating large deviation probability inequalities on the suprema of the Gaussian process which is a generalization of a two-parameter Lévy Brownian motion.     

Inequalities for the weighted mean of -convex functions

In this paper, the inequalities for the weighted mean of -convex functions are established. As applications, inequalities between the two-parameter mean of an -convex function and extended mean values are given.

     

On large increments of a two-parameter fractional Wiener process

In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are of independent interest     

一类具非线性边界条件的高阶方程的双参数奇摄动问题

研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性.     

Functional inequalities for the two-parameter extension of the infinitely-many-neutral-alleles diffusion

By explicitly identifying the transition density function, we derived the super-Poincaré and super-log-Sobolev inequalities for the two-parameter extension of the infinitely-many-neutral-alleles diffusion, which in particular implies the Gross log-Sobolev inequality.     

Existence and multiplicity results for hemivariational inequalities with two parameters

A multiplicity result of Ricceri, based on a minimax inequality, is applied to locally Lipschitz functionals and the existence of one or two non-trivial solutions for a class of two-parameter hemivariational inequalities is proved. An application is given to elliptic problems with discontinuous nonlinearities on unbounded domains.     

Associated random variables and martingale inequalities

Summary Many of the classical submartingale inequalities, including Doob's maximal inequality and upcrossing inequality, are valid for sequences S _j such that the (S _j+1 -S _j's are associated (positive mean) random variables, and for more general demisubmartingales. The demisubmartingale maximal inequality is used to prove weak convergence to the two-parameter Wiener process of the partial sum processes constructed from a stationary two-parameter sequence of associated random variables X _ijwith .Alfred P. Sloan Research Fellow. Research supported in part by NSF Grants MCS 77-20683 and MCS 80-19384     

Large Deviations for Stochastic Volterra Equations in the Plane

We prove a Large Deviation Principle for the family of solutions of Volterra equations in the plane obtained by perturbation of the driving white noise. One of the motivations for the study of such class of equations is provided by non-linear hyperbolic stochastic partial differential equations appearing in the construction of some path-valued processes on manifolds. The proof uses the method developped by Azencott for diffusion processes. The main ingredients are exponential inequalities for different classes of two-parameter stochastic integrals; these integrals are related to the representation of the stochastic term in the differential equation as a representable semimatringale.     

Some properties of random fields related to stochastic integrals with respect to strong martingales

We investigate the properties of random fields related to stochastic intergals with respect to a two-parameter strong square-integrable martingale in the case where the martingale and the integrands depend on the limits of integration. We prove inequalities for the moments of the uniform norm and the modulus of continuity of trajectories of modifications of such fields. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 80–96.