## 留言板

 引用本文: 张石生, 赵烈济, 吴鲜. 概率区间空间中的新型KKM定理及应用*[J]. 应用数学和力学, 1996, 17(11): 951-960.
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

• 摘要: 本文建立了概率区间空间的概念,并在此框架下建立了一个新型的KKM定理。作为应用我们得到了概率区间空间中的一个新的极大极小定理和截口定理,匹配定理及一些重合点定理。所得结果均是全新的,它们不仅包含了Vom Neumann[7]中的主要结果,而且将[1][3～4][6],[8]中的相应结果推广到概率区间空间。
•  [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).

##### 计量
• 文章访问数:  1991
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##### 出版历程
• 收稿日期:  1995-08-30
• 修回日期:  1996-06-20
• 刊出日期:  1996-11-15

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