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.