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.     

Fan Ky不等式的一个新改进

利用Gram矩阵的正定性和可变单位向量建立了Fan Ky不等式的一个新的改进,并且建立了反向Fan Ky不等式.对于非奇异矩阵,得到了Fan Ky不等式以及反向Fan Ky不等式的推广.     

Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities

This paper is intended mainly to present some generic uniqueness results for a class of vector Ky Fan inequalities. By employing the methods of set-valued analysis, we prove that, in the sense of Baire category, most of the problems in a complete metric space, consisting of vector Ky Fan inequalities satisfying some conditions, have unique solution and that every vector Ky Fan inequality, possessing more than one solution, can be approached arbitrarily by a sequence of vector Ky Fan inequalities each of which has a unique solution. Our discussions are under two different settings. One setting is related to vector Ky Fan inequalities defined on a compact set; the other is related to vector Ky Fan inequalities defined on a noncompact set. The corollaries of our results generalized the corresponding results in the literature.     

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.     

Nonlinear separation functions,optimality conditions and error bounds for Ky Fan quasi-inequalities

In this paper, we employ the image space analysis to investigate a Ky Fan quasi-inequality with cone constraints. By means of the oriented distance function, a new nonlinear weak (regular) separation function is introduced. Some necessary and sufficient optimality conditions, especially, a saddle-point sufficient optimality condition for the Ky Fan quasi-inequality with cone constraints, are obtained. By virtue of the nonlinear regular weak separation function, a gap function for the Ky Fan quasi-inequality with cone constraints is obtained. Moreover, we get an error bound for the solution set of the Ky Fan quasi-inequality with respect to the gap function under strongly monotone assumptions.     

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.     

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.     

A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT

In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.     

A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT

In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.     

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     

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.     

关于非凸的有限理性的稳定性

关于有限理性方面的文献, 大多数都是在满足凸性条件下研究有限理性的相关性质, 在一定程度上限制了其应用范围. 应用Ekeland变分原理, 减弱了有限理性模型的假设条件, 考虑在不满足凸性条件下的有限理性模型的稳定性问题. 具体给出了非凸的Ky Fan点问题解的稳定性, 非凸非紧的Ky Fan点问题解的稳定性, 非凸向量值函数Ky Fan点解的稳定性和非凸非紧向量值函数Ky Fan点解的稳定性. 作为应用, 还给出了非凸的n人非合作博弈有限理性模型解的稳定性和非凸的多目标博弈有限理性模型解的稳定性.     

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.     

Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications

In this paper, the image space analysis is employed to study a generalized Ky Fan quasi-inequality with cone constraints. By virtue of a nonlinear scalarization function and a positive linear operator, a nonlinear (regular) weak separation function and a linear regular weak separation function are introduced. Nonlinear and, in particular, linear separations for the generalized Ky Fan quasi-inequality with cone constraints are characterized. Some necessary and sufficient optimality conditions, especially a saddle-point sufficient optimality condition for the generalized Ky Fan quasi-inequality with cone constraints, are obtained. As applications, some sufficient conditions for (weak) vector equilibrium flows of vector traffic equilibrium problems with capacity arc constraints, are derived.     

紧开覆盖的一个新的Ky Fan型匹配定理及其应用

建立了紧开覆盖的一个新的Ky Fan型匹配定理.作为应用,研究了Fan-Browder型重合定理、Ky Fan型最佳逼近定理、极大元定理及超凸空间中的定性对策和抽象经济的平衡存在定理.     

FK-映射的匹配定理及其对约束多目标对策的应用

利用 KKM 技巧,建立了FC-空间中转移紧开值FK-映射的Ky Fan匹配定理.作为应用,获得了FC-空间中的Ky Fan重合定理、约束多目标对策的加权 Nash-平衡和Pareto-平衡的存在定理.     

FC-度量空间中的匹配定理及其对抽象经济的应用

利用KKM技巧,建立了FC-度量空间中转移紧开值映射的Ky Fan匹配定理.作为应用,获得了FC-度量空间中的Ky Fan重合定理、定性对策和抽象经济的平衡存在定理.结论统一、改进和推广了一些近期文献的已知结果.     

Weak and strong convergence of proximal penalization and proximal splitting algorithms for two-level hierarchical Ky Fan minimax inequalities

The theory of Ky Fan minimax inequalities provides a powerful general framework for the study of convex programming, variational inequalities and economic equilibrium problems. One of the fundamental methods for finding a solution of Ky Fan minimax inequalities is the proximal point algorithm, where a lot of papers have been dedicated to this subject. In this paper, a general class of two-level hierarchical Ky Fan minimax inequalities is introduced in real Hilbert spaces. For a wide class of Bregman functions, an association of inexact implicit Bregman-penalization proximal and Bregman-splitting proximal algorithms are suggested and analysed. Weak and strong convergences are proved under essentially weaker conditions. We conclude this paper with a hierarchical minimization problem and a numerical example.     

Lower Semicontinuity of the Solution Mappings to a Parametric Generalized Ky Fan Inequality

In this paper, we investigate weak vector solutions and global vector solutions to a generalized Ky Fan inequality. Under new assumptions, which are weaker than the assumption of strict C-mappings, we establish the lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality by using a scalarization method. These results extend the corresponding ones in the literature. Some examples are given to illustrate our results.     

Some applications of the KKM-mapping principle in hyperconvex metric spaces

In 1996 Khamsi proved a result in hyperconvex metric spaces which is an analogue of the famous KKM-maps principle proved by Ky Fan in 1972 for topological vector spaces.In this note, using the above result due to Khamsi, we establish two results in hyperconvex metric spaces which are analogues of the famous Ky Fan inequality and Sion minimax theorem proved for topological vector spaces in 1972 and 1958, respectively.