Certain Subclasses of Bi-Univalent Functions Associated with the Horadam Polynomials

In Geometric Function Theory, there have been many interesting and fruitful usages of a wide variety of special functions and special polynomials. Here, in this article, we propose to make use of the Horadam polynomials which are known to include, as their particular cases, such potentially useful polynomials as (for example) the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials, the Pell–Lucas polynomials, and the Chebyshev polynomials of the second kind. We aim first at introducing a new class of bi-univalent functions defined by means of the Horadam polynomials. For functions belonging to this new bi-univalent function class, we then derive coefficient inequalities and consider the celebrated Fekete–Szegö problem. We also provide relevant connections of our results with those considered in earlier investigations.