On n-normed spaces
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Date
2016-02-17
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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