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.
出处
《东北师大学报（自然科学版）》
CAS
CSCD
北大核心
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)
