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$q$-norms are really norms

H. Belbachir·M. Mirzavaziri·M. S. Moslehian
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Abstract

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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H. Belbachir, M. Mirzavaziri, M. S. Moslehian. 2005-12-23. $q$-norms are really norms. https://arxiv.org/abs/math/0503616

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