Banach空间的平均强凸性及其对偶性

Average Strong Convexity and Its Dual Property in Banach Spaces

本文证明了Lp（Xi）和X/M空间的平均强凸性，引入了有限阶平均强光滑点的概念，刻划了l∞（X）上有限阶平均强光滑点的特征．

We show that Banach speces sequences Xi are average strongly convex if and only if lp (Xi)is averagestrongly convex. X/M is average strongly convex if M X is approximation subspace, and X is average strongly convex. Wealso characterize finite order average strongly smooth point in l∞ (X).