Abstract.

We want to remark explicitly that, by using the Ln(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 we introduce a new class of analytic bi-univalent functions. Coefficient estimates, Fekete-Szego inequalities and several special consequences of the results are obtained.

Keywords:

Lucas polynomials, coefficient bounds, bi-univalent functions, q-calculus, (p, q)- derivative operator.