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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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##### References:
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