Initial bounds for certain classes of bi-univalent functions defined by the (p, q)-lucas polynomials

Abstract

Our present investigation is motivated essentially by the fact that, in Geometric Function Theory, one can find many interesting and fruitful usages of a wide variety of special functions and special polynomials. The main purpose of this article is to make use of the (p, q)− Lucas polynomials Lp,q,n(x) and the generating function GLp, q, n(x)(z), in order to introduce three new subclasses of the bi-univalent function class Σ. For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete-Szeg¨o inequalities. Some interesting observations of the results presented here are also discussed. We also provide relevant connections of our results with those considered in earlier investigations.