  We consider a bounded radial function f. B. Korenblum and K.E.Zhu give a case
where we have equality between the limit near the boundary of the unit disc of
the Berezin transform and the limit of the normalized Mellin coefficient when
one of them is 0. We previously describe the case where one limit point has
modulus infinite norm of f. We also use the mean values of f near 1. The aim of
this article is to show that between these two extreme cases, we can have
distinct limits. In the same time, we also study the sets of limit points of
these quantities.
