非紧空间及一般点集上极大极小定理

基金项目:

国家及北京市自然科学基金资助项目.

详细信息

Minimax Theorems in Topological Spaces Without Compact and Arbitrary Sets

摘要: 给出了一类非紧空间及一般点集上极大极小定理,首先证明了,X为拓扑空间,Y为任意集时,具有t-拟凸性的泛函f,g:X×Y→R的极大极小比较定理。其次证明了,X和Y均为任意集时,具有t-拟凸性的殆周期泛函f的极大极小定理。
- 极大极小 /
- 拟凸(凹) /
- t-拟凸(凹)
Abstract: In this paper,we give minimax theorems in topological spaces without compact and arbitrary sets. First,we prove a minimax inequality for t-convexlike function f and g on the product set X×Y of a topological space X and an arbitrary set Y.Secondly, we prove a minimax theorem for t-convexlike almost periodic function f on the product set X×Y of two arbitrary sets X and Y.
- minimax /
- convexlike(concavelike) /
- t-convexlike(t-concavelike)