Banach空间中实函数芽的K-bi-Lipschitz等价的判定  

The criterion of K-bi-Lipschitz equivalence of real function germs in Banach spaces

作　　者：许静波[1] 王蕾[2] 陈亮[3] 孙伟志[4] 

机构地区：[1]吉林师范大学数学学院,吉林四平136000 [2]渤海船舶职业学院基础部,辽宁葫芦岛125000 [3]东北师范大学数学与统计学院,吉林长春130024 [4]长春理工大学,吉林长春130022

出　　处：《东北师大学报（自然科学版）》2011年第2期28-32,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10271023);吉林省教育厅"十一五"科学技术研究基金资助项目(2009199)

摘　　要：推广了欧氏空间中的相应概念,给出了Banach空间中实函数芽的K-bi-Lipschitz等价,K-M-bi-Lipschitz等价与相同的切触概念,得到了判别可分的Banach空间上的两个实函数芽为C-bi-Lipschitz等价的一种行之有效的方法.同时指出K-bi-Lipschitz等价与K-M-bi-Lipschitz等价之间的关系.并给出Banach空间上的多项式函数芽在K-bi-Lipschitz等价关系下进行分类的基础.The notions of K-bi-Lipschitz equivalence,the same contact and K-M-bi-Lipschitz equivalence between real function germs in Euclidean spaces are generalized to Banach spaces.The criterion method of C-bi-Lipschitz equivalence between real function germs in separable Banach spaces is given.The relationship of K-bi-Lipschitz equivalence and K-M-bi-Lipschitz equivalence is investigated.The main results provide the basis of the classification of polynomial function germs on Banach space under K-bi-Lipschitz equivalence relation.

关 键 词：BANACH空间 K-bi-Lipschitz等价 K-M-bi-Lipschitz等价 相同的切触 GATEAUX可微 GAUSS测度 

分 类 号：O177.99[理学—数学]