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 ?. 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.