  In this paper, we introduce a couple of classes of functions, denoted by DU
and EB. We present the relationship between them and other known classes. Also,
we show that the elements of the class EB, are amenable and quasi-subadditive
functions (Theorem 2.14). Finally, in the Theorem 2.20, we establish that the
graphic of these elements is contained in the region proposed by J. Dobos and
Z. Piotrowski(see [8]).
