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Coefficient bounds for certain subclasses of meromorphic and bi-univalent functions. (English) Zbl 1331.30011

Summary: In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions \(w=f(z)\) defined on \(\tilde{\Delta}:= \{z \in \mathbb{C}: 1<|z|<\infty\}\) whose inverse \(f^{-1}(w)\) is also univalent meromorphic in \(\tilde{\Delta}\). Estimates for the initial coefficients are obtained for the functions in these new subclasses.

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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