模糊弱伪范数和模糊弱F-空间

发布时间：2018-02-28 21:00

本文关键词： 广义Lasalle伪范数族模糊弱伪范数模糊有界模糊连续模糊弱F-空间　出处：《南京师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：模糊泛函分析是模糊分析学重要的组成部分.而模糊伪赋范线性空间则是模糊泛函分析的重要分支.本文对基于连续的三角模的模糊伪赋范线性空间进行了较为细致地研究,主要内容包含以下三个方面:一、引入模糊弱伪赋范线性空间的概念,并给出广义Lasalle伪范数族的定义.证明了由一个模糊弱伪赋范线性空间可以确定一族广义Lasalle伪范数.相反的,由一族广义Lasalle伪范数可定义一个模糊弱伪赋范线性空间.给出了模糊弱伪赋范线性空间的分明拓扑.二、研究了模糊伪赋范线性空间中的收敛和模糊有界线性算子以及它们之间的关系.在基于一般的连续三角模的模糊伪赋范线性空间中,引入收敛、柯西列、完备、α收敛、α柯西列、α完备的概念、研究了它们之间的关系.引入模糊弱伪赋范线性空间中算子模糊连续、强模糊连续、弱模糊连续、强模糊有界、弱模糊有界的概念,较为深入地研究了上述概念之间的关系.三、引入了模糊弱F-空间的概念,证明了模糊弱F-空间上的分明拓扑与线性运算是相容的.此外,在模糊伪赋范线性空间中引入模糊拓扑,证明了模糊拓扑与线性结构一起成为具有Hausdorff分离的(QL)型拓扑线性空间,且此模糊拓扑弱于由分明拓扑诱导的模糊拓扑.
[Abstract]:Fuzzy functional analysis is an important part of fuzzy analysis, and fuzzy pseudo-normed linear space is an important branch of fuzzy functional analysis. The main contents include the following three aspects: first, the concept of fuzzy weakly pseudo-normed linear space is introduced. The definition of generalized Lasalle pseudo-norm family is given. It is proved that a family of generalized Lasalle pseudo-norm can be determined by a fuzzy weakly pseudo-normed linear space. A fuzzy weakly pseudo-normed linear space can be defined by a family of generalized Lasalle pseudo-norm. The distinct topology of fuzzy weakly pseudo-normed linear space is given. In this paper, convergence and fuzzy bounded linear operators in fuzzy pseudorormed linear spaces and their relations are studied. In fuzzy pseudonormed linear spaces based on general continuous triangular modules, Cauchy series is introduced. The concepts of completeness, 伪 convergence, 伪 Cauchy, 伪 completeness are studied. The concepts of fuzzy continuity, strong fuzzy continuity, weak fuzzy continuity, strong fuzzy boundedness, weak fuzzy boundedness in fuzzy weakly pseudo-normed linear space are introduced. The relation between the above concepts is studied in depth. Thirdly, the concept of fuzzy weak F-space is introduced, and it is proved that the distinct topology on fuzzy weakly F-space is compatible with linear operation. The fuzzy topology is introduced into the fuzzy pseudo-normed linear space. It is proved that the fuzzy topology and the linear structure become the linear spaces with Hausdorff separation and the fuzzy topology is weaker than the fuzzy topology induced by the distinct topology.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177

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