n-赋范空间成为k-光滑空间的一些充要条件  

Some Necessary and Sufficient Conditions for n-normed Space to Become k-smooth Space

作　　者：乌雅罕 苏雅拉图[1] Wuyahan;Suyalatu(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古农业大学学报（自然科学版）》2022年第3期107-110,共4页Journal of Inner Mongolia Agricultural University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11561053);内蒙古师范大学研究生科研创新基金项目(CXJJS18072)。

摘　　要：n-赋范空间是由一般的赋范空间直接推广的一类空间,其光滑性研究是Banach空间几何理论的主要研究内容之一。本文研究了n-赋范空间的k-光滑性问题,并利用Banach空间理论的方法,得到了n-赋范空间为k-光滑的若干特征刻画,所得的结论完善了n-赋范空间的k-光滑性研究。n-normed space is a kind of space directly extended by the general normed space,and its smoothness research is one of the main research contents of Banach space geometric theory. In this paper,the k-smoothness of n-normed space was studied,and some necessary and sufficient conditions for the n-normed space to become k-smooth space by using the Banach space theory were obtained. These results improved the study of k-smoothness of the n-normed space.

关 键 词：n-赋范空间 K-光滑性 有界n-线性泛函 

分 类 号：O177.2[理学—数学]