A quasi-norm is a nonnegative function 
on a vector
space that satisfies 
iff 
,
absolute homogeneity 
,
and a relaxed triangle inequality
 |
for some fixed constant 
(Hussain et al. 2013). It is a norm
when the triangle inequality holds with 
.
For 
, the expression 
is a quasi-norm, but not a norm
in dimensions at least 2. The corresponding integral
means of polynomials on the unit
circle occur in the Baernstein
quasi-norm monotonicity conjecture.
