不动点理论和KKM理论及其应用

发布时间：2018-05-09 10:12

  本文选题：公共不动点定理 + T-KKM定理　； 参考：《西南大学》2016年硕士论文

【摘要】：本文主要研究了一致凸度量空间的公共不动点理论,FWC空间的KKM理论及其应用.全文共分为四个部分：第一章介绍了不动点理论和KKM理论的研究背景和本文的主要工作及其意义.第二章利用一致凸度量空间中的凸性模和自映象对的次相容性,讨论了一类四个自映象的公共不动点的存在性和唯一性问题,得到了公共不动点定理.该结果改进和推广了常见的公共不动点定理.第三章在FWC空间上引入一类广义的T-KKM映象,建立了一些非空紧闭值映象的T-KKM型定理.利用此结果获得了FWC空间中的Fan-Browder不动点定理,Kv Fan截口定理和广义向量均衡问题解的存在性定理.第四章介绍了八类新型的广义向量拟平衡问题系统,利用KKM性质在FWC空间上讨论它们解的存在性.
[Abstract]:In this paper, the common fixed point theory of uniformly convex metric spaces and the KKM theory of FWC spaces and their applications are studied. The thesis is divided into four parts: the first chapter introduces the research background of fixed point theory and KKM theory, and the main work and significance of this paper. In chapter 2, we discuss the existence and uniqueness of common fixed points for a class of four self-mappings by using the subcompatibility of convex modules and self-mapping pairs in uniformly convex metric spaces, and obtain a common fixed point theorem. This result improves and generalizes common common fixed point theorems. In chapter 3, we introduce a class of generalized T-KKM mappings on FWC spaces, and establish some T-KKM type theorems for nonempty closed value mappings. By using this result, the Fan-Browder fixed point theorem and Kv Fan section theorem in FWC spaces and the existence theorem of solutions for generalized vector equilibrium problems are obtained. In chapter 4, eight new classes of generalized vector quasi equilibrium problem systems are introduced. By using KKM property, the existence of their solutions is discussed in FWC space.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O177.91
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本文编号：1865627