An application of differential subordinations. II. (English) Zbl 0711.30023

Obradović, Milutin; Owa, Shigeyoshi

Mat. Vesn. 41, No. 2, 99-102 (1989).

[For part I see Math. Nachr. 147, 61-64 (1990; reviewed above).]
Let A denote the family of analytic functions p defined in the unit disc, with \(p(0)=1\). The basic result of this work is a sufficient condition for the inequality \(| \arg p(z)| <\gamma (\pi /2)\) to hold, where \(\leq \gamma <1\), \(p\in A\). The method of differential subordinations is used in the proof of the above result.

Reviewer: St.Walczak

MSC:

30C45	Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C80	Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30C70	Extremal problems for conformal and quasiconformal mappings, variational methods

Keywords:

differential subordinations