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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)].

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
Full Text: DOI
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