## INITIAL BOUNDS FOR CERTAIN CLASSES OF BI-UNIVALENT FUNCTIONS DEFINED BY THE (p, q)-LUCAS POLYNOMIALS

## INITIAL BOUNDS FOR CERTAIN CLASSES OF BI-UNIVALENT FUNCTIONS DEFINED BY THE (p, q)-LUCAS POLYNOMIALS

*N. Magesh, C. Abirami, S. Altınkaya*

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## 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.

## Keywords

Univalent functions, bi-univalent functions, bi-Mocanu-convex functions, bi- α−starlike functions, bi-starlike functions, bi-convex functions, Fekete-Szego ̈ problem, Chebyshev polynomials, (p, q)-Lucas polynomials.