Banach空间范数的 k-点态粗性和 k-粗性

摘要

对 Banach 空间范数引入了 k-点态粗和 k-粗的概念，利用 Banach 空间理论的方法，给出了 x ∈ S(X)为范数的 k-粗糙点和 X 的范数是 k-粗的一些充分必要条件，证明了(k +1)-粗糙点是 k-粗糙点以及 k-粗糙点与 Fr´echet 可微性的一些结果。特别地，在 k =1的情形下蕴含了关于范数的粗糙点、点态粗范数和粗范数的相应结果%　　In this paper, the k- pointwise rough and k- rough norm on Banach space are introduced. By the method of Banach space theory, the some necessary and sufficient conditions of k- rough point of norm and k-rough norm of X are given respectively. We proved that (k + 1)- rough point is k- rough point and obtained some results related with k- rough point and Fr´echet differentiability. In particular, when k = 1 our results contains the results of about rough point of norm, pointwise rough norm and rough norm.