On the (p, q)-Lucas polynomial coefficient bounds of the bi-univalent function class σ

The idea of the present paper stems from the work of Lee and Aşcı (J Appl Math 2012:1–18, 2012 ). We want to remark explicitly that, in our article, by using the ( p , q )-Lucas polynomials, our methodology builds a bridge, to our knowledge not previously well known, between the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, we aim at introducing a new class of bi-univalent functions defined through the ( p , q )-Lucas polynomials. Furthermore, we derive coefficient inequalities and obtain Fekete–Szegö problem for this new function class.