Fekete-Szegö inequality for bi-univalent functions subordinate to Horadam polynomials (Q2670299)

Summary: Making use of Horadam polynomials, we propose a special family of regular functions of the type \(g(z) = z+ \sum_{j = 2}^\infty d_j z^j\) which are bi-univalent (or bi-schlicht) in the disc \(\{z \in \mathbb{C} : |z| < 1\}\). We find estimates on the coefficients \(|d_2|\) and \(|d_3|\) and 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.