Zhang Shisheng, Yeol Je Cho, Wu Xian. New Version of KKM Theorem in Prohahilistic Metric Spaces with Applications[J]. Applied Mathematics and Mechanics, 1996, 17(11): 951-960.
 Citation: Zhang Shisheng, Yeol Je Cho, Wu Xian. New Version of KKM Theorem in Prohahilistic Metric Spaces with Applications[J]. Applied Mathematics and Mechanics, 1996, 17(11): 951-960.

# New Version of KKM Theorem in Prohahilistic Metric Spaces with Applications

• Rev Recd Date: 1996-06-20
• Publish Date: 1996-11-15
• 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.
•  [1] Zharig Shisheng and Ma Yihai, Generalized KKM theorem on H-space with applications, J. Math. Anal. Appl., 163 (1992), 406-421, [2] 张石生,概率度量空间的基本理论及应用(I),(Ⅱ),应用数学和力学,9(2)(3) (1988). [3] K. Fan,A generalization of Tychonoff's nixed point theorem, Math. Arm., 142(1961),303-310. [4] K. Fan,. Some properties of convex sets related to fixed point theorem, Math. Ann., 266(1984), 519-537. [5] B. Knaster, B. Kuratowski and S. Mazurkiewicz, Ein beweis des fixpunktsatzes für n-dimensionale simplexe, Fund. Math., 14 (19291. 132-137. [6] V. Komorink, Minimax theorems for upper semi-continuous functions, Acra Math. Acad Sci. Hunger, 40 (1982), 159-163. [7] J. von Neumann, Zur theoric der gesellshaftsphiele, Math. Ann., 100(1928), 295-320. [8] S. Park, Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl., 141 (1989), 164-176. [9] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, New York, Amsterdam, Oxford (1992) [10] B. Schweizer and A.Sklar, Probabilistic metric spaces, Pacifis J. Marh., 10 (1960), 313-334. [11] L. L. Stacho, Minimax theorems beyond topological vector spaces, Acta Sci. Math., 42(1980), 157-164. [12] 张石生, Yeol Je Cho, Shin Min Kang, 《概率度量空间和非线性算子理论》,四川大学出版社(1994).

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