Initial Bounds for Certain Classes of Bi-Univalent Functions Defined by Horadam Polynomials

Abstract

The main purpose of this article is to make use of the Horadam polynomials $h_n\left(x\right)$ and the generating function $\mathrm{\Pi }\left(x,z\right)$, in order to introduce three new subclasses of the bi-univalent function class $\sigma .$ For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete–Szegö inequalities. Some interesting observations of the results presented here are also discussed. We also provide relevant connections of our results with those considered in earlier investigations.