K-强凸空间与K-强光滑空间的特征

Characteristics of K-Strongly Convex and K-Strongly Smooth Spaces

文中重新定义了K-强凸空间与K-强光滑空间,讨论了它们的对偶关系,证明了此定义与其它定义的等价关系.用切片刻画了K-强凸空间与K-强光滑空间的特征,进一步完善了Banach空间凸性和光滑性的研究.

In this paper,K-strongly convex space and K-strongly smooth space were redefined,their dual relation was discussed,and the equivalence between this definition and other definitions was proved.The K-strongly convex space and K-strongly smooth space were characterized by slices,which further improved the research on convexity and smoothness of Banach spaces.