$q$-norms are really norms

Details $q$-norms are really norms $q$-norms are really norms

2005-03-26

arxiv.org/abs/math/0503616v2

Aust. J. Math. Anal. Appl. 3 (2006), no. 1, Art. 2, 3 pp.

Mathematics

Functional Analysis

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

Scientific paper

Replacing the triangle inequality, in the definition of a norm, by $|x + y|
^{q}\leq 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.

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