  The Brjuno function was introduced by Yoccoz to study the linearizability of
holomorphic germs and other one-dimensional small divisor problems. The Brjuno
functions associated with various continued fractions including the by-excess
continued fraction were subsequently investigated: it was conjectured that the
difference between the classical Brjuno function and the even part of the
Brjuno function associated with the by-excess continued fraction extends to a
H\"older continuous function of the whole real line. In this paper, we prove
this conjecture and we extend its validity to the more general case of Brjuno
functions with positive exponents.
  Moreover, we study the Brjuno functions associated to the odd and even
continued fractions introduced by Schweiger. We show that they belong to all
$L^p$ spaces, $p\ge1$. We prove that the Brjuno function associated to the odd
continued fraction differs from the classical Brjuno function by a H\"older
continuous function. On the other hand, the Brjuno function associated to the
even continued fraction differs from the classical Brjuno function by a sum of
a H\"older continuous function and a Brjuno-type function associated to the
odd-odd continued fraction, introduced in the study of the best approximations
of the form odd/odd.
