International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 10, Pages 631-639

On n-normed spaces

Hendra Gunawan1 and M. Mashadi2

1Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia
2Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia

Received 6 August 2000; Revised 12 October 2000

Copyright © 2001 Hendra Gunawan and M. Mashadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Given an n-normed space with n2, we offer a simple way to derive an (n1)-norm from the n-norm and realize that any n-normed space is an (n1)-normed space. We also show that, in certain cases, the (n1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the n-norm is equivalent to those in the derived (n1)-norm. Using this fact, we prove a fixed point theorem for some n-Banach spaces.