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On a new subclass of m-fold symmetric biunivalent functions equipped with subordinate conditions. (English) Zbl 1412.30052

Summary: In this paper, we introduce a new subclass of biunivalent function class \(\Sigma\) in which both \(f(z)\) and \(f^{-1}(z)\) are m-fold symmetric analytic functions. For functions of the subclass introduced in this paper, we obtain the coefficient bounds for \(|a_{m+1}|\) and \(|a_{2m+1}|\) and also study the Fekete-Szegö functional estimate for this class. Consequences of the results are also discussed.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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