华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (5): 49-59.

• 应用数学与基础数学 • 上一篇    下一篇

一类二阶逼近集合和二阶逼近导数

廖春美, 李明华   

  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

A Class of second-order approximating sets and derivatives

LIAO Chun-mei, LI Ming-hua   

  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: 首先引入了一类二阶逼近集合和二阶逼近导数. 然后讨论了这些二阶逼近集合之间的关系. 最后利用一种叫做二阶逼近Φ相依集合, 研究了一类集值映射的二阶可微性.

关键词: 二阶逼近导数, 二阶逼近集合, 可微性质

Abstract: A class of second-order approximating sets and second-order derivatives were introduced. The relationships among second-order approximating sets were discussed. Finally, by using so-called second-order approximating Φ-contingent set, second-order differential properties of a class of set-valued maps were investigated.

Key words: second-order approximating derivatives, second-order approximating sets, differential properties

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