n-赋范空间成为k-严格凸的一些充要条件  

Some Necessary and Sufficient Conditions for n-Normed Spaces to be k-Strictly Convex Spaces

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,内蒙古呼和浩特010022

出　　处：《数学的实践与认识》2020年第21期212-220,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(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,其凸性研究是Ba nach空间几何理论的主要研究内容之一.研究了n-赋范空间的k-严格凸性问题并利用Banach空间理论的方法,得到了n-赋范空间为k-严格凸的若干特征刻画所得的结论完善了n-赋范空间的k-严格凸性研究.N-normed spaces are some kinds of spaces directly extended by general normed spaces,and the study on convexity of n-normed spaces is one of the main research contents of geometric theory of Banach spaces.In this paper,we study the k-strict convexity of n-normed spaces and obtain some necessary and sufficient conditions for n-normed spaces to be k-strictly convex spaces by using Banach space theory.These results perfect the study of k-strict convexity of n-normed spaces.

关 键 词：n-赋范空间 k-严格凸性 有界n-线性泛函 

分 类 号：O177.2[理学—数学]