本文關鍵詞： 廣義Lasalle偽范數族 模糊弱偽范數 模糊有界 模糊連續(xù) 模糊弱F-空間　出處：《南京師范大學》2017年碩士論文　論文類型：學位論文

【摘要】：模糊泛函分析是模糊分析學重要的組成部分.而模糊偽賦范線性空間則是模糊泛函分析的重要分支.本文對基于連續(xù)的三角模的模糊偽賦范線性空間進行了較為細致地研究,主要內容包含以下三個方面:一、引入模糊弱偽賦范線性空間的概念,并給出廣義Lasalle偽范數族的定義.證明了由一個模糊弱偽賦范線性空間可以確定一族廣義Lasalle偽范數.相反的,由一族廣義Lasalle偽范數可定義一個模糊弱偽賦范線性空間.給出了模糊弱偽賦范線性空間的分明拓撲.二、研究了模糊偽賦范線性空間中的收斂和模糊有界線性算子以及它們之間的關系.在基于一般的連續(xù)三角模的模糊偽賦范線性空間中,引入收斂、柯西列、完備、α收斂、α柯西列、α完備的概念、研究了它們之間的關系.引入模糊弱偽賦范線性空間中算子模糊連續(xù)、強模糊連續(xù)、弱模糊連續(xù)、強模糊有界、弱模糊有界的概念,較為深入地研究了上述概念之間的關系.三、引入了模糊弱F-空間的概念,證明了模糊弱F-空間上的分明拓撲與線性運算是相容的.此外,在模糊偽賦范線性空間中引入模糊拓撲,證明了模糊拓撲與線性結構一起成為具有Hausdorff分離的(QL)型拓撲線性空間,且此模糊拓撲弱于由分明拓撲誘導的模糊拓撲.
[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, 偽 convergence, 偽 Cauchy, 偽 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.
【學位授予單位】：南京師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O177

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本文編號：1548928