On $(P,Q)-$Lucas Polynomial Coefficients for a New Class of Bi-Univalent Functions Associated with q-Analogue of Ruscheweyh Operator

Abstract

Recently, Fibonacci polynomials, Chebyshev polynomials, Lucas polynomials, Pell polynomials, Lucas–Lehmer polynomials, orthogonal polynomials and other special polynomials became more and more important in the field of Geometric Function Theory. The Theory of Geometric Functions and that of Special Functions are usually considered as very different fields. In this study, by using Lucas polynomials of the second kind, subordination and Ruschewey differential operator,these different fields were connected and a new class of bi-univalent functions was introduced. Also coefficient estimates were obtained for this new class.