On n -normed spaces

Hendra Gunawan and M. Mashadi

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-9

Abstract:

Given an n -normed space with n ≥ 2 , we offer a simple way to derive an ( n − 1 ) -norm from the n -norm and realize that any n -normed space is an ( n − 1 ) -normed space. We also show that, in certain cases, the ( n − 1 ) -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 ( n − 1 ) -norm. Using this fact, we prove a fixed point theorem for some n -Banach spaces.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:965397

DOI: 10.1155/S0161171201010675

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