Banach空间的非常凸性

Very Convexity in Banach Spaces

本文引进非常凸的Banacn空间,讨论了非常凸与弱局部一致凸、弱中点局部一致凸、严格凸的关系,证明了非常凸与非常光滑是对偶概念,并找到了中点局部一致凸及局部完全K凸的对偶概念,推广了文[1]、[2]、[3]中的5个结果.

In this paper,we introduce very convex Banach spaces,discuss the relationship of very convex and weakly locally uniformly rotund. Weakly midpoint locally uniformly convex. Strictly convex,prove that very convex and very smooth is the dual nition. We also find the dual notion of midpoint locally uniformly convex and locally fully k-convex ,generalize five results in[1],[2],[3].