关于概率度量空间中三元公共不动点问题的研究

发布时间：2018-03-25 11:45

本文选题：Menger概率度量空间　切入点：混合概率压缩算子　出处：《南昌大学》2015年硕士论文

【摘要】：概率度量空间利用分布函数来度量元素之间距离.作为推广,对广义Menger概率度量空间和半序概率度量空间中非线性算子的研究也具有非常重要的意义.本文主要研究广义Menger概率度量空间和半序概率度量空间中三元公共不动点与三元重合点问题.全文分为四章.第一章介绍了PM空间的历史背景与预备知识,并简单介绍了本文主要的研究工作.第二章建立了广义Menger概率度量空间, 引入了映射对T:X×X×X→X,A:X→X的三元公共不动点概念.利用伪度量和三角范数的性质,我们对混合概率压缩算子在规函数够条件下的三元公共不动点问题进行了研究.第三章在半序概率度量空间中建立了映射对G:X×X×X→X与g：X→X的相容性概念.在不需要可交换的条件下,研究了相容映射在满足更一般的非线性压缩条件下的三元重合点问题.第四章利用拓扑度方法,在Z-P-S空间中研究了半闭1-集压缩算子的固有值与固有元问题,对相关文献中的结论进行了改进和推广.
[Abstract]:Probability metric space uses distribution function to measure the distance between elements. It is also of great significance to study nonlinear operators in generalized Menger probabilistic metric spaces and semi-ordered probabilistic metric spaces. In this paper, we mainly study ternary common immobility in generalized Menger probabilistic metric spaces and semi-ordered probabilistic metric spaces. The thesis is divided into four chapters. The first chapter introduces the historical background and preparatory knowledge of PM space. In chapter 2, the generalized Menger probabilistic metric space is established, and the mapping pair of T: X 脳 X 脳 X is introduced. 鈫扻,A:X. 鈫扵he concept of ternary common fixed point of X. by using the properties of pseudo metric and trigonometric norm, In this paper, we study the trivariate common fixed point problem of mixed probabilistic contractive operators under the condition of sufficient gauge function. In Chapter 3, we establish a mapping pair of G: X 脳 X 脳 X in a semi-ordered probability metric space. 鈫扻 and g: X. 鈫扵he concept of compatibility of X. Under the condition of no interchangeability, we study the triple coincidence point problem of compatible mappings with more general nonlinear contractions. In chapter 4, we use the topological degree method. In this paper, the eigenvalues and eigenelements of semi-closed 1-set contractive operators are studied in Z-P-S spaces, and the conclusions in related literatures are improved and generalized.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177.91

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