$q$-norms are really norms

Abstract

Replacing the triangle inequality, in the definition of a norm, by $|x+y{|}^q\le 2^{q-1}(|x{|}^q+|y{|}^q)$, we introduce the notion of a q-norm. We establish that every q-norm is a norm in the usual sense, and that the converse is true as well.

3 pages, major changes (title was changed and an author was added due to some improvement)