Differential subordinations for fractional-linear transformations (Q1975939)

Exploiting the ideas due to \textit{S. Miller} and \textit{P. T. Mocanu} [Mich. Math. J. 28, 157-171 (1981; Zbl 0456.30022)] the authors established various relations of the following type: \(\gamma\geq 0\), if the functions \(p(z)+ \gamma zp'(z)\) or \(p(z)+\gamma zp'(z)/p(z)\) are subordinated to \(h(A,B;z)\) in the unit disk then \(p(z)\) is subordinated to a function \(h(\widetilde A,\widetilde B;z)\) (with possibly different parameters), \(h(A,B;z)=(1+Az)(1+Bz)^{-1}\), \(-1\leq B<A\).