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Certain subclasses of analytic and bi-univalent functions. (English) Zbl 1201.30020

Summary: We introduce and investigate two interesting subclasses of normalized analytic and univalent functions in the open unit disk \[ \mathbb U := \{z : z \in \mathbb C \quad \text{and} \quad |z| <1\}, \] whose inverse have univalent analytic continuations to \(\mathbb U\). Among other results, bounds for the Taylor-Maclaurin coefficients \(|a_{2}|\) and \(|a_{3}|\) are found in our investigation.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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