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Coefficients bounds for a family of bi-univalent functions defined by Horadam polynomials. (English) Zbl 1491.30004

Summary: In the present paper, we determine upper bounds for the first two Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\) for a certain family of holomorphic and bi-univalent functions defined by using the Horadam polynomials. Also, we solve Fekete-Szegö problem of functions belonging to this family. Further, we point out several special cases of our results.

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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