Lucas polynomials and applications to an unified calss of bi-univalent functions equipped with (P,Q)-derivative operators

Abstract

We want to remark explicitly that, by using the L-n (x) functions (essentially linked to Lucas polynomials of the second kind), 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, also making use of the differential operator I-p,q(k), we introduce a new class of analytic bi-univalent functions. Coefficient estimates, Fekete-Szego inequalities and several special consequences of the results are obtained.