Abstract
Making use of Horadam polynomials, we propose a special family of regular functions of the typegz=z+∑j=2∞djzjwhich are bi-univalent (or bi-schlicht) in the discz∈ℂ:z<1. We find estimates on the coefficientsd2andd3and the functional of Fekete–Szegö for functions in this subfamily. Relevant connections to existing results and new observations of the main result are also presented.
Highlights
J 2 and S be the set of all members of A that are univalent in D
Swamy and Sailaja [22] have used Horadam polynomials to investigate coefficient estimates for two families of bi-univalent functions, Swamy et al [23] have introduced some subfamilies of Salagean type biunivalent functions subordinate to (m, n)-Lucas polynomials and found initial coefficients, and Wanas and Alina [24] have fixed the Fekete–Szegoproblem for Bazilevic biunivalent function class linked with Horadam polynomials
Inspired by the article [25] and the recent trends on functions in Σ, we present a comprehensive family of Σ associated with Horadam polynomials Hj(x) as in (3) having the generating function (4)
Summary
J 2 and S be the set of all members of A that are univalent in D. Brannan and Taha [5] examined certain well-known subfamilies of Σ in D. e momentum on the study of bi-univalent function family was gained recently, which is due to the work of Srivastava et al [6].
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