發(fā)布時(shí)間：2018-05-09 10:12

  本文選題：公共不動(dòng)點(diǎn)定理 + T-KKM定理�。� 參考：《西南大學(xué)》2016年碩士論文

【摘要】：本文主要研究了一致凸度量空間的公共不動(dòng)點(diǎn)理論,FWC空間的KKM理論及其應(yīng)用.全文共分為四個(gè)部分：第一章介紹了不動(dòng)點(diǎn)理論和KKM理論的研究背景和本文的主要工作及其意義.第二章利用一致凸度量空間中的凸性模和自映象對(duì)的次相容性,討論了一類四個(gè)自映象的公共不動(dòng)點(diǎn)的存在性和唯一性問題,得到了公共不動(dòng)點(diǎn)定理.該結(jié)果改進(jìn)和推廣了常見的公共不動(dòng)點(diǎn)定理.第三章在FWC空間上引入一類廣義的T-KKM映象,建立了一些非空緊閉值映象的T-KKM型定理.利用此結(jié)果獲得了FWC空間中的Fan-Browder不動(dòng)點(diǎn)定理,Kv Fan截口定理和廣義向量均衡問題解的存在性定理.第四章介紹了八類新型的廣義向量擬平衡問題系統(tǒng),利用KKM性質(zhì)在FWC空間上討論它們解的存在性.
[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.
【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O177.91
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本文編號(hào)：1865627