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Differential subordination and superordination of analytic functions defined by the multiplier transformation. (English) Zbl 1170.30008
Summary: Differential subordination and superordination results are obtained for analytic functions in the open unit disc which are associated with the multiplier transformation. These results are obtained by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained.

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