中文摘要：

本文研究了关于ω-强凸空间和ω-强光滑空间的问题.利用Banach理论的方法,证明了ω-强凸空间和ω-强光滑空间是一对对偶概念,并讨论了ω-强光滑性与其它光滑性之间的关系,用切片统一刻画了ω-强凸空间与ω-强光滑空间的特征,完善了ω-强凸空间及其对偶空间的研究.

英文摘要：

In this article,we study problems of about ω-strong convex spaces and ω-strong smooth spaces.Using the method of Banach spaces theory,we show that the ω-strong convex space is just the duality of ω-strong smooth space and study the relation between ω-strong smoothness and various smoothness.Also,the characteristic of ω-strong smoothness or ω-strong convexity is obtained,which is described by the slice of unit sphere.The results perfect the research on ω-strong convex space and its dual space.