Xiao Jianzhong, Zhu Xinghua. Probabilistic Norm of Operators and Resonance Theorems[J]. Applied Mathematics and Mechanics, 1999, 20(7): 729-736.
Citation: Xiao Jianzhong, Zhu Xinghua. Probabilistic Norm of Operators and Resonance Theorems[J]. Applied Mathematics and Mechanics, 1999, 20(7): 729-736.

Probabilistic Norm of Operators and Resonance Theorems

  • Received Date: 1997-01-23
  • Rev Recd Date: 1999-01-21
  • Publish Date: 1999-07-15
  • In this paper,a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced.By means of the probabilistic norm of linear operators,the linear operator theory on probabilistic normed linear space was further studied.On probabilistic normed linear operator space,some resonance theorems dealing with probabilistic bounded sets,probabilistic semi-bounded sets,and probabilistic non-unbounded sets are obtained.
  • loading
  • [1]
    肖建中.M-PN空间上线性算子的概范数与有界性刻画[J].数学研究与评论,1993,13(4):631~632.
    [2]
    张石生.概率度量空间的基本理论及应用(Ⅱ)[J].应用数学和力学,1988,9(3):193~204.
    [3]
    张石生.概率度量空间的基本理论及应用(Ⅰ)[J].应用数学和力学,1988,9(2):117~126.
    [4]
    林熙.概率赋范线性空间的不动点定理[J].数学杂志,1983,3(1):73~76.
    [5]
    Schweizer B, Sklar A. Probabilistic Metric Space[M]. New York, Amsterdam, Oxford: North-Holland,1983.
    [6]
    夏道行,等.泛函分析第二教程[M].北京:高等教育出版社,1987,159~182.
    [7]
    张石生,郭进利.概率线性赋范空间中的概率积分、G1/2teaux微分及Schauder原理[J]. 四川大学学报(自然科学),1989,26(2):127~135.
    [8]
    定光桂.拓扑线性空间选讲[M].南宁:广西教育出版社,1987,43~44.
    [9]
    肖建中、蒋兴国.关于PN空间上线性算子的概率范数[J].应用数学和力学,1997,18(3):285~290.
    [10]
    游兆永,朱林户.概率赋范空间的线性拓扑性质[J].数学进展,1988,17(3):275~279.
    [11]
    Schweizer B, Sklar A. Statistical metric space[J].Prcific Journal of Mathematics,1960,10:313~334.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1722) PDF downloads(723) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return