  In this paper, we discuss new inequalities for accretive matrices through non
standard domains. In particular, we present several relations for $A^r$ and
$A\sharp_rB$, when $A,B$ are accretive and $r\in (-1,0)\cup (1,2).$ This
complements the well established discussion of such quantities for accretive
matrices when $r\in [0,1],$ and provides accretive versions of known results
for positive matrices.
