Differential subordinations for fractional-linear transformations

Abstract

We establish that the differential subordinations of the forms p(z)+γzp′(z)≺h(A1,B1;z) or p(z)+γzp′(z)/p(z)≺h(A2,B2;z) implies p(z)≺h(A,B;z), where γ≥0 and h(A,B;z)=(1+Az)/(1+Bz) with −1≤B<A.