关于复次亚正定矩阵

提出了复次亚正定矩阵的概念，研究了它的基本性质，取得了许多新的结果，建立了与Schur定理、华罗庚定理、Minkowski不等式、Ky Fan不等式、Ostrowski-Taussky不等式、Openheim不等式及华罗庚不等式等相应的重要结果。     

Fan Ky不等式的一个改进

利用改进的H lder不等式并借助于正交矩阵的行列式的积分表示法建立了Fan K y不等式的一个有意义的改进.当A,B为n阶非奇异矩阵时,给出了新创建不等式的一个推广.特别当n=1时,得到了Y oung不等式的一个很强的结果.     

广义Ky Fan点的通有稳定性

得到一个广义的Ky Fan不等式,它以通常的Ky Fan不等式为特例.我们讨论了在一致度量诱导的拓扑结构和二元泛函上方图形的拓扑结构下广义Ky Fan不等式问题构成的空间M中,大多数(在Baire分类意义下)广义Ky Fan不等式问题的所有广义Ky Fan点都是稳定的.     

广义正定矩阵的行列式不等式

研究了广义正定矩阵的行列式理论，给出了一些新的结果，推广了Ky Fan、Openheim、Minkowski、Ostrowski-Taussky等著名行列式不等式，削弱了华罗庚不等式的条件．     

Szasz不等式在亚正定矩阵和拟广义正定矩阵上的推广

实对称正定矩阵的Szasz不等式是Hadamard不等式的加细;本文将Szasz不等式推广到一类亚正定矩阵和拟广义正定矩阵上去,从而推广了关于实对称正定矩阵的Szasz不等式和Hadamard不等式.     

关于矩阵迹的不等式

讨论了满足条件R[A,B]≤1的矩阵和的平方的迹的不等式,并利用经典的H(o|¨)lder不等式和Minkowski不等式,证明了半正定Hermiter矩阵迹的H(o|¨)lder不等式和矩阵迹的Minkowski不等式的推广不等式.     

关于正定矩阵的两个不等式

通过Hermite矩阵的谱分解及一个改进的Young不等式,得到了关于正定矩阵的两个不等式,所得结果是对一些经典的矩阵不等式的进一步推广.最后,作为应用,给出了著名的Holder不等式和Minkowsi不等式的一种反向形式.     

亚半正定矩阵的广义Minkowski不等式的隔离

利用张晗方建立的推广的Hlder不等式和李炯生给出的关于Ostrowskii-Taussky不等式的新刻划,建立了亚半正定矩阵的广义Minkowski不等式的一种隔离,修正并推广了已有结论.     

复矩阵的亚半正定性

复亚半正定矩阵是 Hermite正定阵的推广 ,研究了它的 Kronecker积、Hadamard积和行列式理论 ,将实对称阵的 Schur定理、华罗庚定理、Minkowski不等式、Ky-Fan不等式、Ostrowski-Taussky不等式推广到了一类非 Hermite复矩阵上 ,扩大了 Minkowski不等式的指数范围 ,削弱了华罗庚不等式的条件 .     

非紧集上不连续函数的Ky Fan不等式及其等价形式和应用

证明了非紧集上不具有任何连续性的函数弱Ky Fan点的存在性,给出了在函数只具非常弱的连续性和凸性条件下非紧集上Ky Fan不等式解的存在性,并给出它的两种等价形式.作为应用:(1)得到Ky Fan截口定理和Fan-Browder不动点定理的推广;(2)应用于博弈理论,得到几个新的Nash平衡存在性定理.     

The stability of set of generalized Ky Fan’s points

This paper is concerned with a generalized Ky Fan’s inequality. We first give an existence result of generalized Ky Fan’s (weak) efficient points, and then establish a complete metric space. Based on these results, we obtain the sufficient and necessary conditions of upper semicontinuity of efficient solution mapping to a generalized Ky Fan’s inequality. We also obtain the sufficient conditions of lower semicontinuity and continuity of efficient solution mapping to a generalized Ky Fan’s inequality. Our results are new and different from the corresponding ones in the literature.     

Hölder Continuity for Solution Mappings of Parametric Non-convex Strong Generalized Ky Fan Inequalities

Abstract

This article focuses on a new approach to investigate the Hölder continuity for the solution mapping of a parametric non-convex strong generalized Ky Fan inequality. Based on a non-convex separation theorem, the union relation between the solution set of the parametric non-convex strong generalized Ky Fan inequality and the solution sets of a series of Ky Fan inequalities, is established. Without density results and any information on the solution mapping, a sufficient condition for the Hölder continuity of the solution mapping to the parametric non-convex strong generalized Ky Fan inequality is given by using the key union relation. Our method does not impose any convexity, monotonicity, and the single-valuedness of the solution mapping.     

A Fixed Point Theorem and Some Generalized Ky Fan＇s Minimax Inequalities

In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without ＂local convexity＂. And we also establish some generalized Ky Fan＇s minimax inequalities for set-value vector mappings, which are the generalization of some previous results.     

关于《余A-G型Ky Fan不等式》的发展

Two new proofs of a discrete Ky Fan inequality of the comple mentary A-G type are given. Its continuous version and determinantal analogue on a set of pairwise commutative positive definite matrices are established. A further extension concerning general positive definite matrices of the inequality is also suggested.     

Gap Functions and Error Bounds for Weak Generalized Ky Fan Inequalities

In this paper, we study a weak generalized Ky Fan inequality with cone constraints through image space analysis. First, we characterize the separation for the weak generalized Ky Fan inequality with cone constraints using the saddle points of generalized Lagrangian function. Then, we use regular weak separation functions to construct gap functions and regularized gap functions for the weak generalized Ky Fan inequality with cone constraints in a general way, and establish its error bounds in terms of these gap functions.     

On Some Generalizations and Refinements of a Ky Fan Inequality

In this paper, a Ky Fan inequality and an inequality by Wu and Wang [10] will be generalized. Some new and improved refinements of the Ky Fan inequality will be put forward.AMS Subject Classification (2000) 26D15     

Optimal Control of Elliptic Variational–Hemivariational Inequalities

This paper establishes a bridge between set optimization problems and vector Ky Fan inequality problems. We introduce a general model, called the bifunction-set optimization problem, that provides a unifying framework for the above-mentioned problems. An existence result in our model is obtained, with the help of KKM–Fan’s lemma. As applications, we derive some new or sharper existence results for set optimization problems and generalized vector Ky Fan inequalities with efficient solutions.     

Saddle points and gap functions for weak generalized Ky Fan inequalities

In this paper, we employ the image space analysis method to investigate a weak generalized Ky Fan inequality with cone constraints. Some regular weak separation functions are introduced, and generalized Lagrangian functions are constructed by using these regular weak separation functions. Under suitable convexity assumptions and Slater condition, the existence of solution for the weak generalized Ky Fan inequality with cone constraints is equivalent to a saddle point of the generalized Lagrangian functions. Moreover, we also use the regular weak separation functions to construct gap functions for the weak generalized Ky Fan inequality with cone constraints, and obtain its error bound.