集值B－H－S变分不等式及其应用

本文在Ｄａｎａｃｈ空间中，研究了集值Ｂ－Ｈ－Ｓ变分不等式问题和相补问题．将有限维空间、单值映象的若干结果改进并推广到无穷维空间．利用本文获得的结果．我们解决了无穷维空间中的鞍点问题和两类规划问题．     

Variational Inequality and Complementarity Problem for Set－Valued Mapping with Application

ＶａｒｉａｔｉｏｎａｌＩｎｅｑｕａｌｉｔｙａｎｄＣｏｍｐｌｅｍｅｎｔａｒｉｔｙＰｒｏｂｌｅｍｆｏｒＳｅｔ－ＶａｌｕｅｄＭａｐｐｉｎｇｗｉｔｈＡｐｐｌｉｃａｔｉｏｎ￥ＺｈａｎｇＣｏｎｇｊｕｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｈｕａｉｂｅ...     

弱Orlicz鞅空间的原子分解

本文对于几种类型的弱Orlicz 鞅空间建立了强型和弱型的原子分解定理, 证明了这些空间上的次线性算子的有界性以及这些空间彼此的连续嵌入关系. 弱Orlicz 空间是一类拟Banach 空间, 有关结论扩展了现有的关于Orlicz 空间和弱型Lorentz 空间的相关结论.     

Frechet空间的几个重要不等式

本文给出了Frechet空间中的几个重要不等式，它们是Hilbert空间中的著名极化恒等式在Frechet空间中的情形．推广了Banach空间的许多不等式，且在许多领域中有着各种各样的应用．利用这些不等式，可将许多结果从Banach空间推广到Frechet空间．     

On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

In this paper, the author first introduces the concept of generalized algebraic cone metric spaces and some elementary results concerning generalized algebraic cone metric spaces. Next, by using these results, some new fixed point theorems on generalized (complete) algebraic cone metric spaces are proved and an example is given. As a consequence, the main results generalize the corresponding results in complete algebraic cone metric spaces and generalized complete metric spaces.     

Quasi-Nagata空间的映射定理

本文讨论了quasi—Nagata空间与一类重要广义度量空间k—半分层空间的关系。证明了quasi—Nagata空间的一些映射性质。     

On posets and independence spaces

By constructing a correspondence relationship between independence spaces and posets, under isomorphism, this paper characterizes loopless independence spaces and applies this characterization to reformulate certain results on independence spaces in poset frameworks. These state that the idea provided in this paper is a new approach for the study of independence spaces. We outline our future work finally.     

Real Interpolation of Generalized Besov-Hardy Spaces and Applications

In this paper we consider generalized Hardy spaces which include classical Hardy spaces and Hardy-Lorentz spaces as special cases. We give real interpolation results for such spaces. As applications, we solve an interpolation problem for Besov spaces of generalized smoothness and prove the boundedness of pseudodifferential operators acting both in these spaces and in the local Hardy spaces. For the latter spaces, we also obtain wavelet decompositions.     

几乎第二可数空间、几乎第一可数空间和几乎可分空间

本文定义了几乎第二可数空间,几乎第一数可空间和几乎可分空间,它们分别是第二可数空间,第一可数空间和可分空间的一般化,还研究了这三类新空间以及几乎Lindel?f空间的性质,改进了[2]中的几个定理.     

Double sequence spaces characterized by lacunary sequences

In 1989, Das and Patel considered known sequence spaces to define two new sequence spaces called lacunary almost convergent and lacunary strongly almost convergent sequence spaces, and proved two inclusion theorems with respect to those spaces. In this paper, we shall extend those spaces to two new double sequence spaces and prove multidimensional analogues of Das and Patel’s results.     

A one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space

We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.     

Preference orders and continuous representations

In this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.     

Conditions of regularity in cone metric spaces

In this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions. Among other things, we extend some results of Nguyen [11] from metric spaces to cone metric spaces. The example is included.     

New abstract Hardy spaces

The aim of this paper is to propose an abstract construction of spaces which keep the main properties of the (already known) Hardy spaces H¹. We construct spaces through an atomic (or molecular) decomposition. We prove some results about continuity from these spaces into L¹ and some results about interpolation between these spaces and the Lebesgue spaces. We also obtain some results on weighted norm inequalities. Finally we present partial results in order to understand a characterization of the duals of Hardy spaces.     

Common fixed point theorems for families of compatible mappings in intuitionistic fuzzy metric spaces

In this paper, we prove some common fixed point theorems for any even number of compatible mappings in complete intuitionistic fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces and intuitionistic fuzzy metric spaces.     

Symmetric spaces approach to some fixed point results

In this paper we present a simple and unified approach to the fixed point results on cone symmetric spaces and metric type spaces based on symmetric spaces fixed point theory. We also give a new characterization of semi-metric spaces with open balls.     

拓扑空间、极限空间、及L-拓扑空间之间的关系

给出了极限空间、完备格、拓扑空间、以及L-拓扑空间相互关系的一简要缩述.     

Polar Subspaces and Automatic Maximality

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and its dual. In this paper, we establish several new results and also give improved proofs of some known ones in both the general and the special contexts.     

关于1-序列商映射

引进了1-序列商映射，证明了1-序列商映射象保持sm-第一可数空间．作为这一结果的一个应用，本文证明了几乎开，闭映射保持度量空间，g-度量空间，sm-度量空间．此外本文还证明了度量空间上的1-序列商，紧映射是1-序列覆盖映射．这些结果改进并推广了广义度量空间映射象的有关理论．     

紧致齐性空间上的调和分析（Ⅰ）：富里埃级数的Poisson求和

首先介绍了紧致齐性空间上调和分析的若干基础性结果,并给出这些结果的较简洁的证明。接着,我们定义了紧致齐性空间上函数的卷积(熟知n维球面是一个紧致齐性空间),这一定义看来对研究紧致齐性空间上的调和分析向题是相当有用的。最后,用定义的卷积,研究了紧致齐性空间上Fourier级数的Poisson求和。