k-非常凸、k-非常光滑与(弱)中点局部k-一致光滑空间

k-Very Convex,k-Very Smooth and(Weakly) Midpoint Locally k-Uniformly Smooth Spaces

引入推广的Banach空间的k-非常凸、k-非常光滑、(弱)中点局部k-一致光滑性的概念,讨论了它们与其它k-凸性(k-光滑性)之间的关系,证明k-非常凸性和k-非常光滑性具有对偶性质,(弱)中点局部k-一致光滑性与(弱)中点局部k-一致凸性具有对偶性质.

The generalized notions of k-very convex,k-very smooth and （weakly） midpoint locally k-uniformly smooth are introduced respectively,and the relationship between them and the other k-convex （k-smooth） are discussed. It is proved that there are dual properties between k-very convex and k-very smooth, （weakly）midpoint locally k-uniformly convex and （weakly） midpoint locally k-uniformly smooth respectively.