On n ‐normed spaces

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.