We present analysis of some new means introduced by M. Ra?ssouli and A. Rezgui. We establish comparison relations and results on (K,N)-sub/superstabilizability. Assuming that means involved have asymptotic expansions, we present the complete asymptotic expansion of the resultant mean-map. As an application of the obtained asymptotic expansions and the asymptotic inequality between M and R(Bp,M,Bq), we show how to find the optimal parameters p and q for which M is (Bp,Bq)-sub/super-stabilizable.
Mihokovic et al. (Thu,) studied this question.