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Applied Mathematics and Mechanics (English Edition) ›› 1996, Vol. 17 ›› Issue (11): 1009-1017.

• 论文 •    下一篇

NEW VERSION OF KKM THEOREM IN PROBABILISTIC METRIC SPACES WITH APPLICATIONS

张石生1, 赵烈济2, 吴鲜3   

  1. 1. Sichuan University, Chendu 610064. P. R. China;
    2. Gyeongsang National Univ., Chihju 660-701, Korea;
    3. Yunnan Narmal Univ., Kunmine 650092. P. R. China
  • 收稿日期:1994-05-07 出版日期:1996-11-18 发布日期:1996-11-18
  • 基金资助:

    Project supported by the National Natural Science Foundation of China

NEW VERSION OF KKM THEOREM IN PROBABILISTIC METRIC SPACES WITH APPLICATIONS

Zhang Shisheng1, Yeol Je Cho2, Wu Xiang3   

  1. 1. Sichuan University, Chendu 610064. P. R. China;
    2. Gyeongsang National Univ., Chihju 660-701, Korea;
    3. Yunnan Narmal Univ., Kunmine 650092. P. R. China
  • Received:1994-05-07 Online:1996-11-18 Published:1996-11-18
  • Supported by:

    Project supported by the National Natural Science Foundation of China

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摘要： In this paper we first introduce the concept of probabilistic interval space. Under this framework a new version of KKM theorem is obtained. As application, we utilize this result to study some new minimax theorem. section theorem, matching theorem ,coincidence theorem and fixed point theorem in probabilistic metric spaces. The results presented in this paper not only contain the main resull of von Neumann[7] as its special case but also extend the corresponding resulls of [1, 3, 4, 6, 8] to the case of probabilistic metric spaces.

Abstract: In this paper we first introduce the concept of probabilistic interval space. Under this framework a new version of KKM theorem is obtained. As application, we utilize this result to study some new minimax theorem. section theorem, matching theorem ,coincidence theorem and fixed point theorem in probabilistic metric spaces. The results presented in this paper not only contain the main resull of von Neumann[7] as its special case but also extend the corresponding resulls of [1, 3, 4, 6, 8] to the case of probabilistic metric spaces.

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