International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 225-228
doi:10.1155/S016117129700029X

On subordination of certain subclass of analytic functions

Abstract

In the present paper the class Pn[α,M] consisting of functions f(z)=z+∑k=n+1∞akzz(n≥1), which are analytic in the unit disc E={z:|z|<1} and satisfy the condition |f′(z)+αzf″(z)−1|<M is introduced. By using the method of differential subordination the properties of the class Pα[α,M] are discussed.