  For \alpha in the interval [0,1], we consider the one-parameter family of
\alpha-continued fraction maps, which include the Gauss map (\alpha=1) and the
nearest integer (\alpha=1/2) and by-excess (\alpha=0) continued fraction maps.
To each of these expansions, and to each choice of a positive function u on the
interval I_\alpha=(0,max(\alpha,1-\alpha)) we associate a generalized Brjuno
function B_(\alpha,u)(x). For \alpha=1/2 or \alpha=1, and u(x)=-\log(x), these
functions were introduced by Yoccoz in his work on the linearization of
holomorphic maps. Their regularity properties, including BMO regularity and
their extension to the complex plane, have been thoroughly investigated. We
compare the functions obtained with different values of \alpha and we prove
that the set of (\alpha,u)-Brjuno numbers does not depend on the choice of
\alpha provided that \alpha>0. We then consider the case \alpha=0,
u(x)=-\log(x) and we prove that x is a Brjuno number (for \alpha> 0) if and
only if both x and -x are Brjuno numbers for \alpha=0.
