Fekete–Szegö Inequality for Bi-Univalent Functions Subordinate to Horadam Polynomials

Abstract

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