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Coefficient bounds and Fekete-Szegö inequality for a new family of bi-univalent functions defined by Horadam polynomials. (English) Zbl 1513.30103

Summary: In the current article, we introduce and investigate a new family \(\mathcal{K}_\Sigma(\delta, \lambda, x)\) of analytic and bi-univalent functions by using the Horadam polynomials defined in the open unit disk \(\mathbb{U}\). We determine upper bounds for the initial Taylor-Maclaurin coefficients. Further we obtain the Fekete-Szegö inequality of functions belonging to this family. We also point out several certain special cases for 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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