关于偏度量空间中若干非线性问题的研究-应用数学专业论文.docxVIP

万方数据 万方数据 摘要 摘 要 1994 年,Matthews 在度量空间的基础上提出了偏度量空间的概念，并研究 了偏度量空间中的 Banach 压缩映像原理. 偏度量空间推广了一般意义上的度 量空间，研究偏度量空间中的非线性问题对丰富和发展非线性分析理论有着十 分重要的理论价值和科学意义. 本文主要研究了偏度量空间中几类映射的若干 不动点定理. 全文分为三章. 第一章 介绍了偏度量空间理论与应用的历史背景、现状以及偏度量空间中 的有关概念. 第二章 在偏度量空间中定义了广义 (?, L) -弱压缩映射以及广义 (??, L) -弱 压缩映射，并运用迭代的方法获得了偏度量空间中这两类映射的不动点定理. 第三章 在偏度量空间中提出了映射新的扩张条件，并得到新的扩张映射的 不动点定理，这些结果推广了已有的相关结论. 关键词：偏度量空间；广义 (?, L) -弱压缩；广义 (??, L) -弱压缩；扩张映射；不 动点定理 II Abst Abstract ABSTRACT In 1994, Matthews proposed the concept of partial metric space on the basis of metric spaces, and studied the Banach contraction mapping principle in partial metric space. The partial metric space generalizes the general metric space, the research of the problem of nonlinear in partial metric space contributes important academic value and scientific significance to the enrichment and development the theory of nonlinear analysis. This paper mainly studied some fixed point problems of several kinds of mapping in partial metric spaces. There are three chapters in this thesis. In chapter one, the historical backgrounds and current situation of partial metric space theory and application are introduced and some related concepts of partial metric spaces are given. In chapter two, the generalized ???, L?-weak contraction and generalized (??, L) - weak contraction mappings are defined and some new fixed point theorems for these type contraction mappings are proved by iterative approach in partial metric spaces. In chapter three, some new expanding conditions of mappings are proposed in the partial metric spaces and a new fixed point theorem of expanding mappings is given. These results generalize the existing related conclusions. Key Words: partial metric space; generalized ???, L?-weak contraction; generalized (??, L) - weak contraction ; expanding mapping; fixed point theorem 目录 目录 目 录 HYPERLINK \l _bookmark0 第 1 章 引论 1 HYPERLINK \l _bookmark1 1.1 历史背景与现状 1 HYPERLINK \l _bookmark2 1.2 预备知识 4 第 2 章 偏度量空间中广义弱压缩映射的不动点定理 10 HYPERLINK \