  In the literature there are several methods for comparing two convergent
iterative processes for the same problem. In this note we have in view mostly
the one introduced by Berinde in [Picard iteration converges faster than Mann
iteration for a class of quasi-contractive operators, Fixed Point Theory Appl.
2004, no. 2, 97--105] because it seems to be very successful. In fact, if IP1
and IP2 are two iterative processes converging to the same element, then IP1 is
faster than IP2 in the sense of Berinde. The aim of this note is to prove this
almost obvious assertion and to discuss briefly several papers that cite the
mentioned Berinde's paper and use his method for comparing iterative processes.
