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Two new subclasses of bi-univalent functions. (English) Zbl 1263.30006
The authors give estimates of \(|a_2|\) and \(|a_3|\) for two subclasses of the class of bi-univalent functions \(f\) (\(f\) and the extension of the inverse of \(f\) on the unit disc are univalent) which are derived from the class of \(\alpha-\)convex functions. The “traditional” method of equating coefficients is used.

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