向量值映射的极大极小不等式

华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (5): 42-48.

向量值映射的极大极小不等式

张宇, 陈桃, 徐阳栋

重庆大学数学与统计学院, 重庆 401331

收稿日期:2010-09-01 修回日期:2010-12-01 出版日期:2011-09-25 发布日期:2011-11-22

Minimax inequalities for vector-valued mappings

ZHANG Yu, CHEN Tao, XU Yan-dong

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2010-09-01 Revised:2010-12-01 Online:2011-09-25 Published:2011-11-22

摘要/Abstract

摘要： 利用一类非线性标量化函数和非凸分离定理, 在较弱的条件下, 证明了向量值函数的极大极小定理. 并给出具体例子说明, 所得结果推广了相应文献中的结论.

关键词: 非线性标量化函数, 极大极小不等式, 向量值映射

Abstract: By using a kind of nonlinear scalarization functions and nonconvex separation theorems, under weaker assumptions, the minimax theorem for vector-valued mappings was established. An example was given to illustrate that the result improves the corresponding ones in the literatures.

Key words: nonlinear scalarization function, minimax inequality, vector-valued mapping

中图分类号:

O221.6

张宇, 陈桃, 徐阳栋. 向量值映射的极大极小不等式[J]. 华东师范大学学报(自然科学版), 2011, 2011(5): 42-48.

ZHANG Yu, CHEN Tao, XU Yan-dong. Minimax inequalities for vector-valued mappings[J]. Journal of East China Normal University(Natural Sc, 2011, 2011(5): 42-48.

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