A quasi-norm is a nonnegative function 
on a vector
space 
over the real numbers or complex
numbers that satisfies 
iff 
,
absolute homogeneity 
,
and a relaxed triangle inequality
 |
for some fixed constant 
(Hussain et al. 2013, p. 3).
It is a norm when the triangle
inequality holds with 
.
For 
and a positive
integer 
,
the expression 
is a quasi-norm on 
or 
, but not a norm
when 
. The corresponding integral means
of polynomials on the unit
circle occur in the Baernstein
quasi-norm monotonicity conjecture.
