L p -Version of the Dubins–Savage Inequality and Some Exponential Inequalities

The Dubins–Savage inequality is generalized by using the pth (1<p≤2) conditional moment of the martingale differences. This inequality is further extended under suitable conditions when p>2. Another martingale inequality due to Freedman is also generalized when 0<p≤2. Implications of these inequalities for strong convergence are discussed. Some general exponential inequalities are also given for martingales (supermartingales) under suitable conditions.      

Correlation Inequalities and Applications to Vector-Valued Gaussian Random Variables and Fractional Brownian Motion

In this paper we extend certain correlation inequalities for vector-valued Gaussian random variables due to Kolmogorov and Rozanov. The inequalities are applied to sequences of Gaussian random variables and Gaussian processes. For sequences of Gaussian random variables satisfying a correlation assumption, we prove a Borel-Cantelli lemma, maximal inequalities and several laws of large numbers. This extends results of Be?ka and Ciesielski and of Hytönen and the author. In the second part of the paper we consider a certain class of vector-valued Gaussian processes which are α-Hölder continuous in p-th moment. For these processes we obtain Besov regularity of the paths of order α. We also obtain estimates for the moments in the Besov norm. In particular, the results are applied to vector-valued fractional Brownian motions. These results extend earlier work of Ciesielski, Kerkyacharian and Roynette and of Hytönen and the author.     

广义F-互补问题及其与变分不等式问题的等价性

在Banach空间中引入了一类广义F-互补问题,研究了它与一类变分不等式问题的等价性关系,给出了此类变分不等式问题的解的存在唯一性定理.     

一个含多参量的反向Hilbert型积分不等式

引入权函数,建立一个含多参量与最佳常数因子的新的反向Hilbert型积分不等式.作为应用,给出了其两个等价式及几个特殊结果.     

AN EXTRAGRADIENT METHOD FOR RELAXED COCOERCIVE VARIATIONAL INEQUALITY AND EQUILIBRIUM PROBLEMS

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.     

条件g-期望的矩不等式

找到了几个使条件g-期望的矩不等式在一般意义下成立的关于g和g-期望的充分条件.     

动态供应链网络均衡模型构建与分析

基于单一商品流,考虑了时间变量和库存问题,建立了三层动态供应链网络结构模型.对制造商、零售商和需求市场的多期独立决策行为及其相互作用进行了分析,应用变分不等式构建了各层均衡模型和整个供应链网络均衡模型.最后与相关文献的模型进行了比较.     

关于Mate-Nevai型非线性积分不等式

主要目的是将Mate-Nevai型积分不等式推广到非线性情形,得到了两个具有广泛意义的Mate-Nevai型非线性积分不等式,利用所得结论讨论某些积分方程解的有界性.     

Multivariate irregular sampling theorem

In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.     

具有服务水平的差异产品供应链网络均衡模型研究

顾客服务水平已成为当今企业获取较高市场占有率的重要手段。本文考虑了由多个供应商和多个零售商组成的供应链网络模型,通过制造商和零售商提供的服务水平,零售商的订货满足率以及零售价格等因素较为贴切的刻画消费者的选择偏好,利用变分不等式方法分析了制造商、零售商,需求市场以及整个供应链网络均衡条件,并给出了经济解释。最后,通过算例验证了模型的合理性。