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Differential subordination results for Abbas-starlike function in the upper half-plane. (English) Zbl 1465.30006

Summary: In the present paper, we define new class of analytic functions in the upper half-plane \(D=\{z \in \mathbb{C}: \mathrm{Re}(z)>0\}\). Also, by investigating appropriate classes of admissible functions, we obtain differential subordination results for functions belongs to this new class.

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
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