Horadam Polynomials and a Class of Biunivalent Functions Defined by Ruscheweyh Operator

Abstract

In this paper, we introduce and investigate a class of biunivalent functions, denoted by $\mathcal{H}\left(n,r,\alpha \right)$, that depends on the Ruscheweyh operator and defined by means of Horadam polynomials. For functions in this class, we derive the estimations for the initial Taylor–Maclaurin coefficients $\left|a_2\right|$ and $\left|a_3\right|$. Moreover, we obtain the classical Fekete–Szegö inequality of functions belonging to this class.