矩度量空间中一些压缩映象的不动点定理

发布时间：2018-04-27 03:23

本文选题：偏矩度量空间 + 锥矩度量空间　；参考：《西南大学》2017年硕士论文

【摘要】：2000年Branciari在度量空间的基础上,用四角不等式代替三角不等式提出了矩度量空间的概念,并证明了 Banach压缩映象的不动点定理.随后,许多学者将矩度量空间推广为偏矩度量、锥矩度量、b-矩度量等空间,且在这些空间中研究了若干压缩映象的不动点.本文主要介绍一些广义的矩度量空间的定义,并证明一些压缩映象在这些空间中的不动点定理.共分为四部分:第一章,介绍一些矩度量空间的产生及其不动点理论研究概况,和本文主要研究内容及意义.第二章,介绍偏矩度量空间的相关概念及弱(ψ,φ)压缩映象研究近况,证明带有四个自映象的弱(ψ,φ)压缩映象映象在偏矩度量空间中的公共不动点定理.第三章,介绍锥矩度量空间的相关概念和多值映象的定义及发展近况,并证明一些多值映象在锥矩度量空间中的的不动点定理.第四章,介绍b-矩度量空间的概念及研究现状,并研究b-矩度量空间中(ψ,φ)压缩映象的不动点定理.
[Abstract]:In 2000, on the basis of metric space, Branciari proposed the concept of moment metric space by using four angle inequalities instead of trigonometric inequalities, and proved the fixed point theorem of Banach compression mappings. Then, many scholars extended the moment metric space into moment metric, cone moment measure, b- moment metric space, and studied some pressure in these spaces. The definition of some generalized moment metric spaces is introduced in this paper, and the fixed point theorems of some compressed mappings in these spaces are proved. The first chapter is divided into four parts: the first chapter introduces the production of some moment metric spaces and the research situation of the theory of fixed points, and the main research content and significance in this paper. The second chapter introduces the main contents and significance. The related concept of the moment metric space and the recent research on the weak () compression mappings, prove the common fixed point theorem with the weak (diameter, phi) mappings in the metric space. The third chapter introduces the concept of the cone moment metric space and the definition of the Multivalued Mappings and the recent development, and proves that some Multivalued Mappings are in the cone. The fixed point theorem in moment metric space. The fourth chapter introduces the concept and research status of b- moment metric space, and studies the fixed point theorem of the compressed mappings in the b- moment metric space.

【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.91;O189.11

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