關(guān)于Menger概率度量空間中非線性映射的不動(dòng)點(diǎn)存在性問題研究
發(fā)布時(shí)間：2018-11-23 11:31
【摘要】：本文在Menger PM-空間中提出了許多新的概念.在此基礎(chǔ)上,利用半序方法、迭代方法研究了Menger PM-空間中非線性映射不動(dòng)點(diǎn)的存在性和唯一性問題,獲得許多新的結(jié)果.同時(shí),我們給出了許多例子對(duì)主要結(jié)果進(jìn)行了說明.本文的結(jié)果推廣和改進(jìn)了近期相關(guān)文獻(xiàn)中的不動(dòng)點(diǎn)定理和重合點(diǎn)定理.全文共分為3章.每章的內(nèi)容如下:第1章介紹非線性泛函分析中Menger PM-空間的發(fā)展?fàn)顩r、最新前沿、所要研究的相關(guān)問題,以及給出Menger PM-空間中一些基本概念.第2章在完備的序Menger PM-空間中引入一廣義循環(huán)-弱壓縮映射的概念,并獲得了該映射的一些重合點(diǎn)定理.第3章在廣義Menger PM-空間中定義了(H,Ψ,Φ)-壓縮映射和概率(α,)-壓縮映射,獲得了這兩類映射的一些不動(dòng)點(diǎn)定理,所得結(jié)果推廣和改進(jìn)了許多最近相關(guān)文獻(xiàn)中的結(jié)論.給出了一些具體例子.同時(shí),作為主要結(jié)果的應(yīng)用,研究了一類積分方程解的存在性問題.
[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 (偽,) -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.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O177.91
本文編號(hào)：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 (偽,) -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.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O177.91
【參考文獻(xiàn)】
相關(guān)期刊論文 前1條
1 朱傳喜;朱天;;Z-P-S空間中的若干概率分析問題[J];系統(tǒng)科學(xué)與數(shù)學(xué);2006年01期
，本文編號(hào)：2351440
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