International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 2, Pages 109-117
doi:10.1155/S0161171200001666

Differential subordinations for fractional-linear transformations

Yong Chan Kim1 , Adam Lecko2 , Jae Ho Choi3 and Megumi Saigo3

1Department of Mathematics, Yeungnam University, Gyongsan 712-749, Korea
 2Department of Mathematics, Technical University of Rzeszów, Rzeszów 35-959, Poland
 3Department of Mathematics, Fukuoka University, Fukuoka 814-0180, Japan

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.