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.     

Common fixed points of strict contractions in Menger spaces

The aim of this paper is to prove some common fixed point theorems under certain strict contractive conditions for mappings sharing the common property (E.A) in Menger spaces. As applications to our results, we obtain the corresponding common fixed point theorems under strict contraction in metric spaces. Thus, our results generalize many known results in Menger as well as metric spaces. Some related results are also derived besides presenting several illustrative examples.     

A fixed point theorem in Menger space through weak compatibility

This paper contains a fixed point theorem for six self maps in Menger space. Our result generalizes and extends many known results in Menger spaces and metric spaces.     

强概率收缩对与概率赋范空间中非线性算子方程组的解

在Menger PN空间引入强概率收缩对的概念,并研究了具有强概率收缩对的非线性算子方程组解的存在性和唯一性.这些结果改进和推广了非Archimedean Menger PN空间中相应的结果.     

Menger空间对拟距离空间族的嵌入定理及其应用

在本文中,我们引进了Menger空间中拟距离空间族的嵌入概念并研究了它的一些性质.证明了Menger空间中连续映象序列的一个公共不动点定理.这些映象是假设满足广义的压缩条件的.这里采用的证明方法对于Menger空间的映象而言是一种新的思想.     

Weaker forms of the Menger property in bitopological spaces

Abstract

In this paper we continue previous investigations on the weaker forms of the Menger property in bitopological spaces. We introduce weakly Menger property and study some topological properties of almost and weakly Menger bitopological spaces. We also consider the almost Hurewicz spaces in a bitopological context.     

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.     

HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS IN MENGER PROBABILISTIC NORMED SPACES

We introduce the approximately quadratic functional equation in Menger probabilistic normed spaces. More precisely, we show under some suitable conditions that an approximately quadratic functional equation can be approximated by a quadratic function in above mentioned spaces. Also we consider the stability problem for approximately pexiderized functional equation in Menger probabilistic normed spaces.     

Extension of contractive maps in the Menger probabilistic metric space

In this article, the topological properties of the Menger probabilistic metric spaces and the mappings between these spaces are studied. In addition, contractive and k-contractive mappings are introduced. As an application, a new fixed point theorem in a chainable Menger probabilistic metric space is proved.     

Projective versions of selection principles

All spaces are assumed to be Tychonoff. A space X is called projectively P (where P is a topological property) if every continuous second countable image of X is P. Characterizations of projectively Menger spaces X in terms of continuous mappings , of Menger base property with respect to separable pseudometrics and a selection principle restricted to countable covers by cozero sets are given. If all finite powers of X are projectively Menger, then all countable subspaces of Cp(X) have countable fan tightness. The class of projectively Menger spaces contains all Menger spaces as well as all σ-pseudocompact spaces, and all spaces of cardinality less than d. Projective versions of Hurewicz, Rothberger and other selection principles satisfy properties similar to the properties of projectively Menger spaces, as well as some specific properties. Thus, X is projectively Hurewicz iff Cp(X) has the Monotonic Sequence Selection Property in the sense of Scheepers; βX is Rothberger iff X is pseudocompact and projectively Rothberger. Embeddability of the countable fan space Vω into Cp(X) or Cp(X,2) is characterized in terms of projective properties of X.     

Minimal dynamics on Menger manifolds

The Menger universal spaces are realized as invariant sets of noninvertible, expanding maps. Minimal actions on these spaces of free groups with two or three generators are exhibited.     

A new contraction principle in menger spaces

In the present work we introduce a new type of contraction mapping by using a specific function and obtain certain fixed point results in Menger spaces. The work is in line with the research for generalizing the Banach＇s contraction principle. We extend the notion of altering distance function to Menger Spaces and obtain fixed point results.     

PM-空间中混合压缩的不动点定理与重合点定理

引进了Menger PM-空间中多值情形下的相容映象和弱相容映象概念，并研究了二者之间的联系．在此基础上，获得了Menger PM-空间中若干新的不动点和重合点定理．最后，给出了这一结果在度量空间中的应用．     

Selection principles in relator spaces

Recently, Ko?inac introduced selection principles and games in relator spaces and suggested a systematic study in this area. In this paper we will present some basic results considering the relator Menger and relator Hurewicz properties following some ideas from [12].     

On Countable-Dimensional Spaces with the Menger Property, Rational Dimension and a Question of S. D. Iliadis

 This paper deals with the class of spaces which are countable unions of zero-dimensional sets and with the larger class of Haver’s C-spaces. All spaces are assumed to be separable and metrizable. We are concerned with various aspects of universality of these classes when they are combined with the covering analogue for σ-compactness defined by Menger and the rational dimension introduced by Menger and N?beling. A solution of a problem of S. D. Iliadis [16] concerning universal spaces for rational dimension will result. Received 11 September 1998; in revised form 12 January 1999     

M-PN 空间中的非线性问题

在MengerPN空间中构造新的边界条件,采用新的技巧,通过拓扑度理论给出几类非线性算子方程解的存在性定理,改进了以往若干结论,并将所得的结果应用到一类特殊的函数方程中．     

Multivalued generalizations of probabilistic contractions

We generalize some well-known fixed point theorems for probabilistic contractions to multivalued contractions. The contraction maps are considered in generalized Menger spaces.     

Common fixed point theorems under strict contractive conditions in Menger spaces

The main purpose of this paper is to establish some common fixed point theorems under strict contractive conditions for mappings satisfying the property (E.A) in Menger probabilistic metric spaces. As applications, we obtain the corresponding common fixed point theorems under strict contractive in metric spaces.     

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。     

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.