作 者: ;
机构地区: 华南师范大学南海校区学院数学系
出 处: 《华南师范大学学报(自然科学版)》 2003年第1期18-23,共6页
摘 要: 给出δ -强凸函数和几乎δ -强凸函数的定义 ,研究它们的稳定性 ,获得了δ -强凸函数一致地逼近一个强凸函数、几乎δ -强凸函数在线性Lebesgue测度意义下几乎处处一致地逼近一个强凸函数及几乎强凸函数几乎处处等于一个强凸函数等 3个重要结果 . Definitions of δ-strongly convex function and almost δ-strongly convex function are given. Their stabilities are investigated and three important results are obtained: a δ-strongly convex function approaches a strongly convex function uniformly; an almost δ-strongly convex function approaches a strongly convex function almost everywhere uniformly under the sense of linear Lebesgue measure, and an almost strongly convex function equals a strongly convex function almost everywhere.