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Coefficient estimates for a certain subclass of analytic and bi-univalent functions. (English) Zbl 1244.30033
Summary: We introduce and investigate an interesting subclass \(\mathcal{H}_{\Sigma}^{h,p}\) of analytic and bi-univalent functions in the open unit disk \(\mathbb{U}\). For functions belonging to the class \(\mathcal{H}_{\Sigma}^{h,p}\), we obtain estimates on the first two Taylor-Maclaurin coefficients \(|a_{2}|\) and \(|a_{3}|\). The results presented in this paper generalize and improve some recent work of the last author, A.K. Mishra and P. Gochhayat [ibid. 23, No. 10, 1188–1192 (2010; Zbl 1201.30020)].

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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