中文摘要：

该文引入了两类新的Banach空间，即k接近一致光滑空间和ω接近一致光滑空间，它们分别是Denka Kutzarova所引入的k接近一致凸空间和ω接近一致凸空间的对偶空间．作为主要结果，得到了这两类Banach空间的特征刻画及一些性质，弄清了k一致光滑空间、k接近一致光滑空间、ω接近一致光滑空间，完全k光滑空间和接近一致光滑空间的蕴涵关系．

英文摘要：

In this paper, we introduce two new classes of Banach spaces： k nearly uniformly smooth spaces and w nearly uniformly smooth spaces, which are the dual notions to k nearly uniformly convex spaces and ω nearly uniformly convex spaces respectively, introduced by Denka Kutzarova. We give some characters and properties of these two kinds of Banach spaces. Apart from that we really distinguish the k uniformly smooth spaces, k nearly uniformly smooth spaces, ω nearly uniformly smooth spaces, fully k smooth spaces and nearly uniformly smooth spaces.