K-强凸与局部K一致光滑空间

K STRONGLY CONVEX AND LOCALLY K UNIFORMLY SMOOTH SPACES

本文引进Ｋ－强凸与局部Ｋ一致光滑Ｂａｎａｃｈ空间，讨论了局部Ｋ一致凸．Ｋ－强凸．中点局部Ｋ一致凸、Ｋ－严格凸之间的关系，证明了Ｋ－强凸与Ｋ－强光滑、局部Ｋ一致凸与局部Ｋ一致光滑是对偶概念。

In this paper,we introduce K strongly convex and locally K uniformly smooth in Banach spaces.We discuss the relationship of locally K uniformly rotund.K strongly convex.midpoint locally K uniformly convex and K strictly convex,prove that K strongly convex and K strongly smooth is the dual notion.We also prove that locally K uniformly smooth spaces is K strongly smooth spaces.