广义Hilbert不等式的改进

通过引入一个形如π/sin πp -θ/n1 1r(r =p ,q)的权系数改进了广义Hilbert不等式 ,其中θ是一个正实数 ,其最佳值是 :θ =ln2 - 434 8+ξ192 0 (3742 <ξ <6 136 72 ) .

关于Hilbert不等式的一个改进(英文)

证明了重组数的经典Hilbert重不等式通过引入一个适当的形如π－θ／（θ＞0）的权函数可以把两个单独的和都得到改进。借助于Euler—Maclaurin求和公式得到了一个非常强的结果。

关于广义Hilbert双重级数不等式

本文建立了两个新型的广义Hilbert双重级数不等式.

Hilbert不等式的推广

本文讨论了一个在不等式理论中占重要地位的不等式－Ｈｉｌｂｅｒｔ不等式。由于Ｈｉｂｅｒｔ不等式在解析函数论、单实变函数论等数学分支的广泛应用，人们对它进行了许多研究和推广。本文应用推广的Ｈｏｌｄｅｒ不等式给出Ｌｅｖｉｎ和Ｓｔｃｃｋｉｎ￣［６］及Ｌｅｖｉｎ￣［７］在许多数下Ｈｉｌｂｅｒｔ不等式的推广。

关于带权的Hilbert不等式的一个上确界(英文)

在这篇文章中，Hilbert不等式被进一步加强，讨论了形上的权函数、证明了与序列有关的常数λ＝1．4603545+是θ的上确界，从而使文[2]中所提出的一个问题（徐利治猜想）得到解决。

关于hilbert－ingham不等式和它的应用

本文给出（ｉ）ｈｉｌｂｅｒｔ不等式和ｈｉｌｂｅｒｔ－ｉｎｇｈａｍ不等式一些有意义的共同改进；（ｉｉ）一些ｆｅｊｅｒ－ｒｉｅｓｚ型不等式的改进和（ｉｉｉ）ｈａｒｄｙ不等式的改进．

Hilbert不等式和Witten ζ 函数

1.引言 在本文中，我们在回顾那些源自Hilbert（希尔伯特），Hardy（哈代）和其他一些人的优美的不等式的同时，探讨在分析，数论和算子理论之间的种种有趣的联系。我们首先讨论刚才提到的希尔伯特不等式（[14]，[18]），然后将它应用于各种多重ζ-值。由此，在经典数学的数值和符号计算的相互交汇过程中，

积分型Hilbert定理的改进与应用

本文建立如下权函数的不等式ｗ （ｘ） ＝ ∫∞０１ｘ ＋ ｙ ＋ １（ｘ ＋ １ｙ ＋ １）１／２ｄｙ ≤π［１ － １ － ２／π（ｘ ＋ １）１／２］ （ｘ ∈［０，∞）），这里，常数１－ ２／π是最佳值，从而改进了积分型Ｈｉｌｂｅｒｔ定理，作为应用，建立一个Ｈｉｌｂｅｒｔ类积分不等式及其加强式；并改进推广了Ｈａｒｄｙ－Ｌｉｔｔｅｗ ｏｏｄ 积分不等式．

On the Generalizations of Hilbert’s Inequality

In this paper,by employing a refined Cauchy’s inequality,some strengthened Hilbert’s inequality with parameter A,B,λ are further improved.

A General Projection Method for a System of Relaxed Coercive Variational Inequalities in Hilbert Spaces

In this paper,we consider a new algorithm for a generalized system for relaxed coercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods.Our results include the previous results as special cases extend and improve the main results obtained by many others.

Sharp constants for a class of multilinear integral operators and some applications

We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basic functions. Using the integral, we can easily calculate the sharp constants for the multilinear Hilbert inequality, the generalized Hardy-Littlewood-Sobolev inequality and the multilinear Hardy operator.

A GENERAL ITERATIVE METHOD OF FIXED POINTS FOR EQUILIBRIUM PROBLEMS AND OPTIMIZATION PROBLEMS

The purpose of this paper is to present a general iterative scheme as below：{F（un,y）＋1/rn（y-un,un-xn）≥0,y∈C,xn＋1=（I-αnA）Sun＋αnγf（xn）and to prove that, if {an} and {rn} satisfy appropriate conditions, then iteration sequences {xn} and {un} converge strongly to a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solution of a variational inequality, too. Furthermore, by using the above result, we can also obtain an iterative algorithm for solution of an optimization problem min h（x）, where h（x） is a convex and lower semicontinuous functional defined on a closed convex subset C of a Hilbert space H. The results presented in this paper extend, generalize and improve the results of Combettes and Hirstoaga, Wittmann, S.Takahashi, Giuseppe Marino, Hong-Kun Xu, and some others.