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 Geo- metric 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-Szego ̈ 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.