Banach空间的近-凸性和近-光滑性  

Near Convexity and Near Smoothness in Banach Space

作　　者：陈卓谦 魏文展 CHEN Zhuo-qian;WEI Wen-zhan(School of Mathematics and Statistics,Guangxi Teachers Education University,Nanning 530299,China)

机构地区：[1]广西师范学院数学与统计科学学院,广西南宁530299

出　　处：《广西师范学院学报（自然科学版）》2018年第1期21-23,46,共4页Journal of Guangxi Teachers Education University(Natural Science Edition)

基　　金：广西自然科学基金(0728050)

摘　　要：引入了Banach空间近-非常极凸(近-drop凸)和近-非常极光滑(近-强光滑)的概念.讨论了近-非常极凸(近-drop凸)和近-非常极光滑(近-强光滑)的对偶关系,从拓扑结构和单位球切片的几何结构的角度刻画了近-非常极凸空间.In this paper,we introduce a new convexity and a new smoothness in Banach space which is near very extremely convexity and near very extremely smoothness.We also prove the duality between them and redefine the near very extremely convex space by its topological structure and geometry,respectively.Our proofs also complete the research of the convexity and smoothness of the Banach space.

关 键 词：近-非常极凸 近-drop凸 近-非常极光滑 近-强光滑 

分 类 号：O177.2[理学—数学]