局部凸空间k-极凸性和k-极光滑性  

k-Extreme Convexity and k-Extreme Smoothness in Locally Convex Spaces

作　　者：申守伟[1] 魏文展[1] 季乐文[1] 

机构地区：[1]广西师范学院数学科学学院,广西南宁530023

出　　处：《广西师范学院学报（自然科学版）》2013年第2期25-28,共4页Journal of Guangxi Teachers Education University(Natural Science Edition)

基　　金：广西自然科学基金资助项目(0728050)

摘　　要：引入了局部凸空间中k-极凸性和k-极光滑性这一对对偶概念,然后讨论与其它k-极凸性和k-极光滑性之间的关系,并给出了它们在P-自反的条件下的等价对偶定理.In this paper, the dual notions of k-- extreme convexity and k-- extreme smoothness are introduced in locally convex spaces, which are generalization of both k-- extreme convexity（k-- extreme smoothness）in Banach spaces. The relationship between them and the other convexity （smoothness） are discussed. In addition, on the conditions of P-- reflexivity, we obtain further the equivalent dual theorem of between k--extreme convexity and k--extreme smoothness.

关 键 词：k-极凸性 k-极光滑性 偶对 P-自反 

分 类 号：O177.2[理学—数学]