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On certain generalizations of \(\mathcal{S}^\ast(\psi )\). (English) Zbl 1493.30025

Summary: In this paper, we consider functions analytic in the unit disk that are subordinate to functions of the same type that are defined by certain differential subordinations. We prove several sharp majorization theorems and a product theorem.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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