KKM技巧及其应用

本文介绍KKM技巧,并用以建立了新的抉择定理和重合定理,它们是[2,10,11,15,16]等近期文献中一些重要结果的推广.     

Generalized KKM-type theorems for weakly generalized KKM mapping with some applications

In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.     

Equivalent forms of a generalized KKM theorem and their applications

In this paper, we study various types of variational relation problems. We establish the existence of solutions for these types of problems and point out some important particular cases and their applications. We also show that some existence theorems of solution for these types of problems and some existence theorems of variational inclusion problems are equivalent to a generalized KKM theorem. Applying our results we obtain existence theorems of common fixed point, generalized maximal element theorems, a generalized coincidence theorems and a section theorem.     

一类新的KKM定理及其应用*

本文得到一类新的KKM定理,统一和改进了[2,3,0,7,11]中的结果。作为应用,我们得到了几个匹配定理、重合定理、不动点定理、极大极小不等式定理及截口定理。     

KKM Type Theorems and Coincidence Theorems with Applications to the Existence of Equilibria

In this paper, we obtain some coincidence theorems and some KKM-type theorems. We apply these results to establish the existence of the solution to generalized vector equilibrium problems, where a bimap f : X × Y 2^Z is involved and some sufficient conditions are imposed on f.     

L-空间中的KKM映射及不动点定理

引入了L-空间和L-空间上的KKM类映射，建立了关于该类映射的一些不动点定理，其中包括Schauder型和Fan-Browder型不动点定理．得到了L-空间中的KyFan匹配定理和叠合点定理．     

G-凸空间中的KKM定理，匹配定理和截口定理

在G-凸空间中证明了一些新的KKM型定理．作为应用,在G-凸空间中得到了一些新的匹配定理和截口定理,所得结果改进和推广了[2,3,7]中的相关结果．     

Coincidence theorem for admissible set-valued mappings and its applications in FC-spaces

A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.     

预拓扑空间中的KKM型定理

本文研究了预拓扑空间中的KKM型定理.利用定义预有限连续空间及预FC-KKM映象类,获得了预FC-空间中的几种类型的KKM型定理.推广了拓扑窄问中几种类型的KKM型定理到预拓扑空间中.     

拓扑空间中的KKM型定理和重合点定理

引入了一类新的有限连续空间(简称, $FC$-空间),并在$FC$-空间中证明了一些新的涉及容许类集值映射和具有紧局部交性质的KKM型定理和重合点定理.作为应用,在$FC$-空间中得到了一些新的不动点定理.这些结果统一和推广了近期文献在抽象凸空间中的一些重要结果.     

Generalized KKM type theorems in FC-spaces with applications (II)

This paper is a continuum of the preceding paper of author. By applying a coincidence theorem in noncompact FC-space without any convexity structure due to author, a new KKM type theorem is first proved under noncompact setting of FC-spaces. The equivalent relation between the coincidence theorem and the KKM type theorem is also established. As applications of the KKM type theorem, we establish some new existence theorems of solutions for three classes of generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.     

广义KKM定理的推广

本文给出了更一般的广义 KKM定理 ,使定理更简洁 ,应用更广泛和方便     

Generalized KKM theorems,minimax inequalities,and their applications

This paper extends the well-known KKM theorem and variational inequalities by relaxing the closedness of values of a correspondence and lower semicontinuity of a function. The approach adopted is based on Michael's continuous selection theorem. As applications, we provide theorems for the existence of maximum elements of a binary relation, a price equilibrium, and the complementarity problem. Thus our theorems, which do not require the openness of lower sections of the preference correspondences and the lower semicontinuity of the excess demand functions, generalize many of the existence theorems such as those in Sonnenschein (Ref. 1), Yannelis and Prabhakar (Ref. 2), and Border (Ref. 3).The author is grateful to Professor Franco Giannessi for helpful comments and suggestions.     

A generalization of the classical sphere theorem

In this paper, we prove a sphere theorem for Riemannian manifolds with partially positive curvature which generalizes the classical sphere theorem.

     

A generalization of the remainder theorem and factor theorem

We propose a generalization of the classical Remainder Theorem for polynomials over commutative coefficient rings that allows calculating the remainder without using the long division method. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school students.     

一般化凸空间上KKM定理的另一种形式及其应用

§1Introductionandpreliminaries In1929,Knaster,Kuratowski,andMazurkiewicz(simply,KKM)[1]deducedthe celebratedKKMtheorem.TheKKMtheory,firstcalledbySehiePark,isthestudyof applicationsofvariousequivalentformulationsoftheclassicalKKMprinciple[2].Atthe beginning,thetheorywasmainlystudiedonconvexsubsetsofHausdorfftopologicalvector spaces[3],butlater,ithasbeenextendedtoconvexspacesbyLassonde[4],andtospaces havingcertainfamiliesofcontractiblesubsets(simply,C-spacesorH-spaces)by Horvath[5].Mor…     

Minimax-type inequalities for a family of functions with applications

In the present paper there are given a number of minimax-type inequalities for a family of functions, involving two multivalued mappings, one being strongly decomposable and the other monotone. Hence some applications to the variational-type inequality theory and to the fixed point theory. Supported both by the National Natural Science Foundation of China and by the Institute of Mathematics, Academia Sinica     

Constrained open mapping theorem with applications

We prove a generalization of Graves? Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a set-valued one having particular properties. The nonlinear mapping is restricted to a closed convex subset of a Banach space. We apply the results to derive necessary and sufficient conditions ensuring the existence of a differentiable selection for the inverse mapping. A slight generalization of a sufficient condition by J. Klamka on so-called constrained exact local controllability of nonlinear and semi-linear dynamic systems is also proved.     

A generalization of a theorem of Heins

Let be the family of holomorphic selfmaps of the unit disk in the complex plane . Heins established the continuity of the functional which assigns to ( denotes the identity map) either (i) the fixed point of or (ii) the limit of its iterations or (iii) if ( represents the boundary of ). Using an Abate extension of the Denjoy-Wolff lemma to strongly convex domains, we extend this result of Heins to selfmaps of strongly convex domains in with boundary.