带有单模糊映射的一般变分不等式解的存在性

众所周知，在各种变分不等式问题中，解的存在性是最基础也是最重要的问题之一．本文的目的是在Hilbert空间中研究带有单模糊映射的一般变分不等式解的存在性．此外，还讨论了几种特殊情况．     

Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters

In this paper, the problem of stochastic stability for a class of time-delay Hopfield neural networks with Markovian jump parameters is investigated. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Without assuming the boundedness, monotonicity and differentiability of the activation functions, some results for delay-dependent stochastic stability criteria for the Markovian jumping Hopfield neural networks (MJDHNNs) with time-delay are developed. We establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities.     

Lyapunov-type inequalities for nonlinear systems

In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations.     

Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational conclusions of set-valued bifunctions on convex subsets of Banach spaces with applications

In this paper, variational conclusions of set-valued bifunctions on convex subsets of Banach spaces are investigated and several new results are obtained. The results are applied to the fixed point theory and variational inequalities. We obtain two fixed point theorems and existence theorems of solutions of variational inequalities.     

Continuous modified Newton’s-type method for nonlinear operator equations

A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point x ₀ and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated. Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003 This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks DAAD for support     

几何凸函数与琴生型不等式

给出几何凸函数的定义以及判定几何凸函数的方法 ,建立关于几何凸函数的琴生型不等式 ,最后给出它的应用 ,包括改进一些已知不等式和建立一些新不等式 .     

Bager第五图的完善

１９８９年发表的Ｂａｇｅｒ第五图，包含关于三角形元素的３５个二次规范画数之间的５１个不等式通过细致的分析，本文给出了其中遗漏的１２个基本不等式     

Some integral inequalities inN independent variables

Some new linear and nonlinear integral inequalities of Volterra-type inn independent variables are established. They improve and contain the main results of A. Corduneanu^[7] which in turn extend a number of known results in the literature. An application to certain initial value problem of partial differential equation is also indicated.     

Banach空间值鞅不等式与弱大数定律

本文证明了Ｂａｎａｃｈ空间值鞅的一些不等式，讨论了Ｂａｎａｃｈ空间的凸性及光滑性与某些鞅不等的式的联系，给出了Ｈｉｌｂｅｒｔ空间的一个鞅不等式刻划，同时还讨论了一致Ｐ光滑空间中鞅的弱大数定律，本文的结论推广与改进了很多熟知的定理。