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Coefficient estimates for a general subclass of \(m\)-fold symmetric bi-univalent functions. (English) Zbl 1435.30055

Summary: In the present paper, we introduce and investigate an interesting subclass \({\mathcal B}_{{\Sigma}_m}^{h,p}(\lambda,\gamma)\) of \(m\)-fold symmetric bi-univalent functions in the open unit disk \(\mathbb{U} \). Furthermore, we obtain estimates on the coefficients \(|a_{m+1}|\) and \(|a_{2m+1}|\) for functions belonging to this subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

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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