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New subclasses of bi-univalent functions. (English) Zbl 1218.30024
Summary: We introduce two new subclasses of the function class \(\varSigma \) of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients \(|a_{2}|\) and \(|a_{3}|\) for functions in these new subclasses.

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