n-Banach空间中点列的强收敛与弱收敛

The Strong and Weak Convergence of Sequence in n-Banach Spaces

在文献[1]的基础上,将2-赋范空间中强收敛与弱收敛的相关结果推广到了n-Banach空间中.首先,在n-赋范空间中引进了点列的弱收敛,一致凸与凸性模等概念,得到了n-Banach空间中强收敛与弱收敛的基本性质.其次,讨论了n-Banach空间中强收敛与弱收敛之间的关系.最后,给出了n-Banach空间成为一致凸空间的两个充要条件.

In this paper,the results of 2-normed spaces according to reference [1] are generalized to n- Banach spaces. Firsly, the conceptions of weak convergence, uniformly convex and modulus of convexity are introduced in n-normed spaces; secondly, it is shown that the relations of strong convergence and weak convergence;finally, two necessary and sufficient conditions for n-Banach spaces to be uniformly convex spaces are obtained.