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

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.