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

• 应用数学与基础数学 • 上一篇    下一篇

向量值映射的极大极小不等式

张 宇, 陈 桃, 徐阳栋   

  1. 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   

  1. 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: 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

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