概率区间空间中的新型KKM定量及应用

本文建立了要概率区间空间的概念，并在此框架下建立了一个新型的ＫＫＭ定理，作为应用我们得到概率区间空间中的一个新的极大极小定理和截口定理，匹配定理及一些重合点定理。     

概率度量空间中一个新的不动点定理

概率度量空间中压缩型映象不动点定理的研究开始于1972年Schgal-Bharucha-Reid的工作[3]。以后不少人对概率度量空间中映象的不动点定理进一步讨论,特别是Istratescu的工作[4]把[3]中的结果作了重要的推广。最近张石生[2]对[3]、[4]中的结果作了进一步的推广,[2]中的结果包含了[3]、[4]的主要结果。 在此基础上,本文给出概率度量空间中压缩型映象的一个新的不动点定理。文中涉及的概念及引用的基本定理均见[1]。     

SST空间中压缩映射的几个不动点定理

本文给出了SST概率度量空间中压缩型映射的几个不动点定理,改进并推广了张石生[2],方锦暄[3]及陈肇姜[4]中的许多重要结果.     

概率准度量族空间（英文）

引入了概率准度量族空间、概率准范数族空间、随机准度量族空间和随机准范数族空间的概念，包括了现有的各种相关空间类[1～11]（特别是[8，9]）作为特殊情况，建立了统一的空间体系．同时，我们研究了所引入的一般空间类的一些性质和拓扑结构．     

概率n-度量空间中的不动点定理

本文引进了概率 n-度量空间 ,并将 [1 ]、[2 ]的某些主要结果拓广至 Menger概率 n-度量空间     

区间空间中的非紧极大极小定理

本文得到了区间空间中两类非紧极大极小定理．其结果不仅包含了引文[1-10]中的相应结果为特例，而且发展和改进了[6]中的相应结果．     

概率度量空间中的Ekeland变分原理与集值映象的Caristi重合定理

借助偏序方法,本文得到概率度量空间中之一推广形式的Ekeland变分原理及一集值形式的Caristi重合定理,同时证明了这两个定理之间的等价性.本文结果是[1,2,5,6,7,9]中相应结果的改进和推广.     

概率逻辑学基本定理在多值命题逻辑系统中的推广

通过引入概率测度空间,在n值Lukasiewicz命题逻辑系统中提出了满足Kolmogorov公理的命题公式的概率;证明了概率逻辑学基本定理,并将概率逻辑学基本定理推广到了更一般的形式,改进了对推理结论的不可靠度上界的估计;将概率逻辑学的基本方法引入计量逻辑学,建立了更一般的逻辑度量空间;通过概率逻辑学基本定理,证明了逻辑度量空间中概率MP,HS规则,它是真度MP,HS规则的推广.     

非连续的增算子的不动点定理及其对含间断项的非线性方程的应用

<正> 本文是作者工作[1]的继续. 关于增算子的不动点定理,在数学的许多领域,特别是在非线性微分方程和非线性积分方程中,有着广泛的应用(见[2][3]L4][5][6]).设E是Banach空间,P是E中的锥,D=[u_o,ν_o]是E中的序区间,A:D→E是增算子,满足u_o≤Au_o,Au_o≤ν_o.关于增算子的三个有代表性的结论是:     

概率度量空间的基本理论及应用(Ⅱ)*

本文是作者文章[1]的继续.得出了概率度量空间的集合的各种概率有界性的表征.借助于这些结果及[1]中所得结果,讨论了概率线性赋范空间中的线性算子理论及概率度量空间映象的不动点定理.     

A Fixed Point Theorem for Multi—valued Composite Increasing Operators

Ａ　Ｆｉｘｅｄ　Ｐｏｉｎｔ　Ｔｈｅｏｒｅｍ　ｆｏｒ　Ｍｕｌｔｉ－ｖａｌｕｅｄ　Ｃｏｍｐｏｓｉｔｅ　Ｉｎｃｒｅａｓｉｎｇ　ＯｐｅｒａｔｏｒｓＬｉＦｅｎｇｙｏｕ（李凤友）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｔｉａｎｊｉｎ＇ＮｏｒｍａｌＵｎｉ...     

Banach空间中广义正交分解定理与广义正交可补子空间

本文首先将 Ｈｉｌｂｅｒｔ空间中的Ｒｉｅｓｚ正交分解定理推广到 Ｂａｎａｃｈ空间,得到 Ｂａｎａｃｈ空间广义正交分解定理．然后,利用此定理讨论由Ｊａｍｅｓ Ｒ．Ｃ．［１］引入的Ｂａｎａｃｈ空间中正交概念及 Ｎａｓｈｅｄ Ｍ．Ｚ．［２］引入的 Ｂａｎａｃｈ空间中（广义）正交可补子空间,得到判别子空间广义正交可补的充分必要条件,并由此给出Ｈｉｌｂｅｒｔ空间的一个新特征．     

A Fixed Point Theorem for Multi-valued Composite Increasing Operators in Partially Ordered Spaces

DefinitionlLl]I,etXbeaHausdorffTopologicalspacewhichhaspartiallyorderedstructure.WesayXisasemiorderedTopologicalSpace,ifforanytwonets{x.Ir6T}and{YrlrET}inX,x,相似文献   

The maximum genus, matchings and the cycle space of a graph

In this paper we determine the maximum genus of a graph by using the matching number of the intersection graph of a basis of its cycle space. Our result is a common generalization of a theorem of Glukhov [5] and a theorem of Nebeský [15].     

Banach空间闭子集上微分方程解的整体存在唯一性定理

本文利用比较方法和Kuratowski非紧致测度研究Banach空间闭子集上微分方程解的整体存在唯一性,得出了一个一般性判别准则.作为特例,本文的结果包含了文[4]中的主要定理.     

FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES (Ⅱ)

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i(A,Ω, p) is equal to nonzero, where i(A,Ω, p) is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point the-orems of the completely continuous and weakly inward mapping, which generalize...     

A Generalization of the One-Step Theorem for Matrix Polynomials

In this paper we give a new proof of Krein's Theorem for orthogonal matrix polynomials based on a "one-step" version of the theorem. This parallels the proof given in [3] of Krein's Theorem in the scalar case.     

Nonlinear random elliptic boundary value problem

In this paper we obtain a solvability result for random elliptic boundary value problem. Our result extends Browder's [2] main theorem to the random case. We use author's [4] fixed point theorem for this purpose.     

S. G Mikhlin (1908 – 1990)

Our concern is to find a representation theorem for operators in B(c(X), c(Y)) where X and Y are Banach spaces with Y containing an isomorphic copy of c₀. Cass and Gao [1] obtained a representation theorem that always applies if Y does not contain an isomorphic copy of c₀. Maddox [3], Melvin - Melvin [4], and Robinson [5] consider operators in B(c(X), c(Y)) that are given by matrices. In this paper we show that Cass's and Gao's result in [1] can be extended, when Y contains an isomorphic copy of c₀, to certain operators that we call represent able. In addition, we show that when Y contains an isomorphic copy of co there are always operators that fall outside the scope of our representation theorem. Light is also cast on a theorem given in Maddox [3, Theorem 4.2] and [5, Theorem IV].     

A Cyclic Probabilistic C-Contraction Results using Hadzic and Lukasiewicz T-Norms in Menger Spaces

In this paper, we introduce generalized cyclic C-contractions through p num-ber of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t-norm. In our next theorem we use Lukasiewicz t-norm. Our results generalize the results of Choudhury and Bhandari [11]. A control function [3] has been utilized in our second theorem. The results are illustrated with some examples.