关于Menger概率度量空间中非线性映射的不动点存在性问题研究
发布时间：2018-11-23 11:31
【摘要】：本文在Menger PM-空间中提出了许多新的概念.在此基础上,利用半序方法、迭代方法研究了Menger PM-空间中非线性映射不动点的存在性和唯一性问题,获得许多新的结果.同时,我们给出了许多例子对主要结果进行了说明.本文的结果推广和改进了近期相关文献中的不动点定理和重合点定理.全文共分为3章.每章的内容如下:第1章介绍非线性泛函分析中Menger PM-空间的发展状况、最新前沿、所要研究的相关问题,以及给出Menger PM-空间中一些基本概念.第2章在完备的序Menger PM-空间中引入一广义循环-弱压缩映射的概念,并获得了该映射的一些重合点定理.第3章在广义Menger PM-空间中定义了(H,Ψ,Φ)-压缩映射和概率(α,)-压缩映射,获得了这两类映射的一些不动点定理,所得结果推广和改进了许多最近相关文献中的结论.给出了一些具体例子.同时,作为主要结果的应用,研究了一类积分方程解的存在性问题.
[Abstract]:In this paper, many new concepts are proposed in Menger PM- spaces. On this basis, the existence and uniqueness of fixed points of nonlinear mappings in Menger PM- spaces are studied by means of the semi-ordered method and iterative methods, and many new results are obtained. At the same time, we give many examples to illustrate the main results. The results of this paper extend and improve the fixed point theorem and coincidence point theorem in recent literature. The full text is divided into three chapters. The contents of each chapter are as follows: chapter 1 introduces the development of Menger PM- space in nonlinear functional analysis, the latest frontier, the related problems to be studied, and some basic concepts in Menger PM- space. In chapter 2, we introduce a concept of generalized circulation-weakly contractive mapping in a complete ordered Menger PM- space, and obtain some coincidence point theorems of the mapping. In chapter 3, we define (H, 蠄, 桅) -contractive mappings and probabilistic (伪,) -contractive mappings in generalized Menger PM- spaces, and obtain some fixed point theorems for these mappings. The results extend and improve the conclusions in many recent literatures. Some concrete examples are given. At the same time, the existence of solutions for a class of integral equations is studied.
【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
本文编号：2351440
[Abstract]:In this paper, many new concepts are proposed in Menger PM- spaces. On this basis, the existence and uniqueness of fixed points of nonlinear mappings in Menger PM- spaces are studied by means of the semi-ordered method and iterative methods, and many new results are obtained. At the same time, we give many examples to illustrate the main results. The results of this paper extend and improve the fixed point theorem and coincidence point theorem in recent literature. The full text is divided into three chapters. The contents of each chapter are as follows: chapter 1 introduces the development of Menger PM- space in nonlinear functional analysis, the latest frontier, the related problems to be studied, and some basic concepts in Menger PM- space. In chapter 2, we introduce a concept of generalized circulation-weakly contractive mapping in a complete ordered Menger PM- space, and obtain some coincidence point theorems of the mapping. In chapter 3, we define (H, 蠄, 桅) -contractive mappings and probabilistic (伪,) -contractive mappings in generalized Menger PM- spaces, and obtain some fixed point theorems for these mappings. The results extend and improve the conclusions in many recent literatures. Some concrete examples are given. At the same time, the existence of solutions for a class of integral equations is studied.
【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
【参考文献】
相关期刊论文 前1条
1 朱传喜;朱天;;Z-P-S空间中的若干概率分析问题[J];系统科学与数学;2006年01期
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