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

Abstract

The idea of the present paper stems from the work of Lee and Asci (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–Szego problem for this new function class.