Applied Mathematics and Mechanics (English Edition) ›› 1988, Vol. 9 ›› Issue (2): 123-133.

• 论文 • 上一篇    下一篇

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅰ)

张石生   

  1. Department of Mathematics, Sichuan University, Chengdu
  • 收稿日期:1987-01-09 出版日期:1988-02-18 发布日期:1988-02-18
  • 基金资助:

    Projects supported by the Science Fund of the Chinese Academy of Sciences

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅰ)

Zhang Shi-sheng   

  1. Department of Mathematics, Sichuan University, Chengdu
  • Received:1987-01-09 Online:1988-02-18 Published:1988-02-18
  • Supported by:

    Projects supported by the Science Fund of the Chinese Academy of Sciences

摘要: This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space) are given and the characterizations of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to study the linear operator theory and fixed point theory on PM-spaces.

关键词: p(x)-Laplacian, differential inclusion problem, three-critical-point theorem

Abstract: This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space) are given and the characterizations of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to study the linear operator theory and fixed point theory on PM-spaces.

Key words: p(x)-Laplacian, differential inclusion problem, three-critical-point theorem

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