拓扑空间中新的广义L-KKM型定理及其应用

In this paper, some new generalized L-KKM type theorems with finitely open values and with finitely closed values are established without any convexity structure in topological spaces. As applications, some new matching theorem, fixed point theorem and existence the orem of equilibrium problem with lower and upper bounds are also given under some suitable conditions. These theorems presented in this paper unify and generalize some corresponding known results in recent literatures.     

ON POINTWISE R-SUBWEAKLY COMMUTING MAPS AND BEST APPROXIMATIONS

The main purpose of this paper is to prove some common fixed point theorems for pointwise R-subweakly commuting maps on non-starshaped domains in p-normed spaces and locally convex topological vector spaces. As applications, invariant approximation results are established. This work provides extension as well as substantial improvement of several results in the existing literature.     

I-模糊拓扑空间中的紧度

In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly.     

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.     

关于广义Bergman空间的乘子

In this paper,we characterize the multipliers of generalized Bergman spaces Ap,q,αwith 00) in almost every case considered. The corollaries on multipliers of the spaces Ap,q,αextend some related results.     

A Unified Fixed Point Theory in Generalized Convex Spaces

Let B be the class of ＇better＇ admissible multimaps due to the author. We introduce new concepts of admissibility （in the sense of Klee） and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.     

The Stable Farkas Lemma for composite convex functions in infinite dimensional spaces

In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.     

CHARACTER, DENSITY AND CELLULARITY OF L-FUZZY TOPOLOGICAL SPACES

In this paper we generalize the notions of weight,character, density and cellularity of topological spaces to L-fuzzy topogical spaces. We prove theorems corresponding to some of usual theorems. In particular we generalize Hewitt-Marczewski-Pondiczery theorem on the density of the product of topological spaces to the case of L-fuzzy topological spaces (Theorem 4. 4). We also discuss the relations between topological spaces and its induced fuzzy topological spaces for these cardinal functions.     

纤维拓扑空间理论简介

Fibrewise topological spaces theory,presented in the recent 20 years,is a new branch of mathematics developed on the basis of General Topology,Algebra topology and Fibrewise spaces theory.It is associated with differential geometry,Lie groups and dynamical systems theory.From the perspective of Category theory,it is in the higher category of general topological space,so the discussion of new properties and characteristics of the variety of fibre topological space has more important significance.This paper introduces the process of the origin and development of Fibrewise topological spaces theory.Then,we study the main contents and important results in this branch.Finally,we review the research status of Fibrewise topological spaces theory and some important topics.     

A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces

Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in topological vector spaces is defined, and their fundamental properties are presented. The relationships between the cone bounded quasiconvex mapping defined in this paper and cone convex mapping, and other known cone quasiconvex mapping are also discussed.     

有序拓扑向量空间中的共鸣定理

本文研究有序拓扑向量空间中非线性映照的共鸣定理．对于取值于有序拓扑向量空间中的映照，利用序关系，引入了一类广泛的非线性映照．对于这类非线性映照，应用纲理论，并给出了关于点态序有界蕴涵一致序有界的共鸣定理．     

乘积Banach空间中等式约束向量极值问题的最优性必要条件

本文利用Banach空间中的隐函数定理和序线性拓扑空间中对于次似凸向量值映射的择一定理,得出了乘积Banach空间中具有等式约束向量极值问题的若干最优性必要条件.     

关于对半层空间

利用对$g$-函数和半连续函数给出对半层空间的一些刻画, 并讨论了具有半层拓扑的拓扑序$C$-空间的对半层性.     

拓扑序空间中的广义向量值均衡问题

利用一个KKM型定理,在拓扑序空间中,建立了关于广义向量值均衡问题解的某些新的存在性定理.     

集值映射向量最优化的最优性条件

本文在序线性拓扑空间中,证明了广义Y+一次似凸集值映射的一个择一性定理,利用此定理,我们得到集值映射向量最优化问题的最优性条件.     

Many Familiar Categories can be Interpreted as Categories of Generalized Metric Spaces

The simple concepts of (general) distance function and homometry (a map that preserves distances up to a calibration) are introduced, and it is shown how some natural distance functions on various mathematical objects lead to concrete embeddings of the following categories into the resulting category DIST°: quasi-pseudo-metric, topological, and (quasi-)uniform spaces with various kinds of maps; groups and lattice-ordered abelian groups; rings and modules, particularly fields; sets with reflexive relations and relation-preserving maps (particularly directed loop-less graphs and quasi-ordered sets); measured spaces with Radon-continuous maps; Boolean, Brouwerian, and orthomodular lattices; categories with combined objects, for example topological groups, ordered topological spaces, ordered fields, Banach spaces with linear contractions or linear continuous maps and so on.     

取值于拓扑向量空间的准齐性算子族的共鸣定理

本文给出了取值于局部有界拓扑向量空间的准齐性算子族的共鸣定理,进而给出了从桶形 空间到一般局部凸空间的准齐性拟凸算子族的共鸣定理.     

Topological vector spaces admissible in economic equilibrium theory

In models of economic equilibrium in markets with infinitely many commodities, the commodity space is an ordered topological vector space endowed with additional structure. In the present paper, we consider ordered topological vector spaces which are admissible (for equilibrium analysis) in the sense that every economy which is reasonably well behaved posesses an equilibrium. It turns out that this condition may be characterized in terms of topology and order. This characterization implies that the commodity space has the structure of a Kakutani space.     

序线性空间中向量极值问题的最优性条件

本文在序线性空间中建立了广义次似凸映射下的择一定理,运用此定理,得出一类向量极值问题的最优性条件.     

拓扑线性空间中的Drop定理与Drop性质

给出了拓扑线性空间中的一个Drop定理.利用此Drop定理,证明了拓扑线性空间中的每个序列紧凸集具有Drop性质;每个可数紧闭凸集具有拟Drop性质.而且结出了拓扑线性空间中Drop性质和拟Drop性质的序列流特征.也讨论了Drop性质和拟Drop性质与泛函取极值之间的联系.