$q$-norms are really norms

H. Belbachir, M. Mirzavaziri, M. S. Moslehian

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-…