A normed vector space 
is said to be uniformly
convex if for sequences 
, 
, the assumptions 
, 
, and 
together imply that
 |
as 
tends to infinity.
Such spaces are important in functional analysis. For example, the classical Banach-Saks theorem
can be generalized so that the desired conclusion holds in the case that 
is a Banach space whose conjugate
space (that is, the complex conjugate of the
dual vector space 
) is uniformly convex.
