山东理工大学学报（自然科学版）Issue(6)：12-16,5.
关于映射一致可微性的几个定理
Some theorems on uniform differentiability of mapping
摘要
Abstract
It is important and difficult to study the concept of uniform differentiability in analysis . The sufficient and necessary condition for it is usually discussed in the one-dimension .In this pa-per ,we extended to the high-dimension ,and showed that the mapping is uniform differential if and only if the differential operator (i .e .,the matrix operator ) of mapping is uniform continuous in the sense of operator norm .Meanwhile ,we also gave a equivalent condition for judging the u-niform continuous to matrix operator ,i .e .,every element of matrix is uniform continuous .Fur-thermore ,we considered it in infinite dimensional ,and proved that if the mapping is C1 in ε0 -neighborhood of compact set ,it will be uniform differential in a δ1 (<ε0 )-neighborhood .关键词
一致可微/有限维/无穷维/映射Key words
uniform differentiability/finite dimension/infinite dimension/mapping分类
数理科学引用本文复制引用
钟延生..关于映射一致可微性的几个定理[J].山东理工大学学报（自然科学版）,2013,(6):12-16,5.基金项目
国家自然科学基金资助项目（11026208）；福建省自然科学基金资助项目（2012J05002）；博士后基金资助项目 （）
