直觉Menger空间中的广义压缩映射原理及其在微分方程中的应用

利用Atanassov的思路,将直觉Menger空间定义为由Menger提出的Menger空间的自然推广.同时也得出一个新广义压缩映射,并运用该压缩映射证明了直觉Menger空间中微分方程解的存在性定理.     

Pretopologies, preuniformities and probabilistic metric spaces

Summary A pretopology on a given set can be generated from a filter of reflexive relations on that set (we call such a structure a preuniformity). We show that the familly of filters inducing a given pretopology on Xform a complete lattice in the lattice of filters on X. The smallest and largest elements of that lattice are explicitly given. The largest element is characterized by a condition which is formally equivalent to a property introduced by Knaster--Kuratowski--Mazurkiewicz in their well known proof of Brouwer's fixed point theorem. Menger spaces and probabilistic metric spaces also generate pretopologies. Semi-uniformities and pretopologies associated to a possibly nonseparated Menger space are completely characterized.     

关于随机共轭空间的各种定义及随机线性泛函各种有界性的某些评论

中心目的是详细廉政论在随机共轭空间理论形成过程中所经历的三个阶段的工作，尤其指出了这三个阶段工作之间的联系及本质差别；给出了强有界、拓扑有界及几乎处处有界随机线性泛函之间的关系；亦指出了在概率赋范空间上线性算子理论研究中目前存在的不足．     

概率度量空间中广义β-可容许映射的二元重合点定理及其应用

在Menger PM-空间中,引入广义β-可容许映射的概念。在不要求两映射可交换的情况下,利用迭代法,建立了广义β-可容许映射的二元重合点定理。获得了一些新的结果,推广和改进了相关文献中的不动点定理和二元重合点定理。最后,给出了主要结果的一个应用。     

关于随机赋范模中最佳逼近的一个注记

证明了随机赋范模中一个点是其任一子模的依概率范数的弱最佳逼近点当且仅当它是该子模的依概率范数的最佳逼近点,亦当且仅当该点是该子模的依随机范数的最佳逼近点.利用这些关系我们可以借助于随机赋范模的最近进展获得许多概率赋范空间中的新的最佳逼近定理.     

Some remarks on functions with values in probabilistic normed spaces

In this paper we consider an enlargement of the notion of the probabilistic normed space. For this new class of probabilistic normed spaces we give some topological properties. By using properties of the probabilistic norm we prove some differential and integral properties of functions with values into probabilistic normed spaces. As special cases, results for deterministic and random functions can be obtained.      

Generalized contraction mapping principle and differential equations in probabilistic metric spaces

A new generalized contraction mapping principle in probabilistic metric spaces is obtained. As an application, we utilize this principle to prove the existence theorems of solutions to differential equations in probabilistic metric spaces. All the results presented in this paper are new.

     

直观随机赋范空间中三次泛函方程的稳定性

先引入直观随机赋范空间的概念．然后,借助这一概念,然后对任意的三角范数在该空间的框架下,研究了三次泛函方程的稳定性．另外,还介绍了随机空间理论、直观空间理论及泛函方程理论间的密切关系．     

关于Fuzzy赋范空间的若干问题（Ⅱ）

在1984年,吴从炘、方锦暄和A.K.Katsaras分别提出了两种Fuzzy赋范空间的定义。这些概念既是赋范空间概念的自然推广,又是特殊的Fuzzy拓扑线性空间。在文[3～5]中,不仅考察了这两种定义之间的关系,还讨论了Fuzzy赋范空间的性质以及其上广义Fuzzy线性算子的连续性等。在本文中,我们将继文[4]给出Fuzzy赋范空间中子集有界性、稠密性的刻划条件并利用这些条件给出Fuzzy范数是诱出的充要条件。此外,作为诱出Fuzzy范数的推广,我们给出了两类Fuzzy范数的特征刻划。     

A Short and Partial History of Probabilistic Normed Spaces

This contribution aims at presenting a survey of a portion of the theory of Probabilistic Normed spaces. No result will be proved, so that the reader is referred to the original sources for the proofs. The theory of PN spaces has many facets and touches on many branches of mathematics, for instance, geometry, functional analysis, topology, probability. This justifies the adjective “partial” that appears in the title. Therefore, it is perhaps better to declare from the start what one may expect from this survey. It is only natural to investigate which “classical”properties of normed spaces are preserved in the new setting. But it is probably more interesting to look for those properties that pertain to the new theory and which have no corresponding analogue in the classical theory. It must also be added that Probabilistic Normed spaces may be approached from different standpoints: they may be studied for their own sake, as a special subject in functional analysis or in topology that is worth investigating simply because it is there, or because it provides a tool to approach open problems or, again, to shed light on topics that one thought had been thoroughly investigated. In this, one thinks immediately of the possible applications in probability and statistics. This paper was written as a part of the project “Metodi stocastici in finanza matematica” of the Italian M.I.U.R..     

Morse-Palais lemma for nonsmooth functionals on normed spaces

Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.

     

Common fixed point theorems for expansion mappings in various spaces

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc. In the memory of 65^th birthday anniversary of his Father Late Sh. Ram Phool Sharma     

概率赋范空间上的一些不动点定理的进一步分析

该文在局部有界ＰＮ空间或邻域卜局部凸ＰＮ空间上,证明了非空完备子集上的概率压缩映象必有唯一不动点;并在度量线性空间中给出了关于伪范族一致压缩映象的不动点定理．     

Accretive operators which are always single-valued in normed spaces

Set-valued accretive operators in Banach spaces have been extensively studied for several decades. Our main purpose in this paper is to establish a quite revealing result that says that every set-valued lower semi-continuous accretive mapping defined on a normed space is, indeed, single-valued on the interior of its domain. No reference to the well-known Michael’s Selection Theorem is needed. This result is used to extend known theorems concerning the existence of zeros for such operators, as well as showing existence of solutions for variational inclusions.     

关于线性算子的概率范数与算子空间

由于满足(PN-5)条件的PN空间(E,F)就是MangerPN空间(E,F,min),因此,肖建中等给出的关于PN空间上线性算子概率范数的结果有较大的局限性.本文中,在较一般的MengerPN空间上研究有关线性算子的概率范数和算子空间的问题,改进和推广了肖建中等的结果.     

概率收缩偶与非阿基米德Menger概率赋范空间中非线性方程组的解*

本文在非阿基米德Menger概率赋范空间中引入了概率收缩偶的概念,研究了非阿基米德Menger概率赋范空间中具概率收缩偶的非线性方程组的解的存在性与唯一性.发展和改进了引文[1～5]的相应结果.     

Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces

We investigate the analytic regularity of the Stokes problem in a polygonal domain with straight sides and piecewise analytic data. We establish a shift theorem in weighted Sobolev spaces of arbitrary order with explicit control of the order-dependence of the constants. The shift-theorem in the framework of countably weighted Sobolev spaces implies in particular interior analyticity and Gevrey-type analytic regularity near the corners.     

广义H-空间的理论及其应用*

本文给出了广义H-空间的完备性特征性质和紧性特征性质,同时也研究了这一空间的度量化定理.作为这些理论的应用.我们得到了Menger概率度量空间的完备性特征和紧性特征.给出了该空间的度量化函数的具体形式.