On an application of certain sufficient condition for starlikeness. (English) Zbl 1155.30009

Sokół, Janusz

J. Math. Appl. 30, 131-135 (2008).

Summary: We consider a sufficient condition for function to be \(\alpha\)-starlike function, when \(\alpha\in[0,1/2]\). We use it for certain subclass of strongly starlike functions defined by a geometric condition. We take advantage of the techniques of differential subordinations.

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

Jack’s lemma; convex function; \(k\)-starlike function; strongly starlike function; convolution