概率区间空间中的新型KKM定理及应用<sup>*</sup>

概率区间空间中的新型KKM定理及应用^*

基金项目: * 国家自然科学基金

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。
- 概率度量空间 /
- 概率区间空间 /
- 可链W-链 /
- 重合点
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.
- probabilistic metric space /
- probabilistic interval space /
- chainabilily /
- W-chainability

[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).