Banach空间范数的k-点态粗性和k-粗性  

k- pointwise roughness and k- roughness on Banach spaces

作　　者：义德日胡[1] 苏雅拉图[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《纯粹数学与应用数学》2012年第4期553-558,共6页Pure and Applied Mathematics

基　　金：国家自然科学基金(11061022)

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Fréchet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 suffcient conditions of k-rough point of norm and krough 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 Fréchet differentiability.In particular,when k = 1 our results contains the results of about rough point of norm,pointwise rough norm and rough norm.

关 键 词：k-粗糙点 k-点态粗 k-粗 k-粗指数 BANACH空间 

分 类 号：O177.2[理学—数学]