Faber Polynomial Expansion for a New Subclass of Bi-univalent Functions Endowed with $(p,q)$ Calculus Operators

Abstract

In this paper, we use the Faber polynomial expansion techniques to get the general Taylor-Maclaurin coefficient estimates for $|a_n|,\ (n\geq 4)$ of a generalized class of bi-univalent functions by means of $(p,q)-$calculus, which was introduced by Chakrabarti and Jagannathan. For functions in such a class, we get the initial coefficient estimates for $|a_2|$ and $|a_3|.$ In particular, the results in this paper generalize or improve (in certain cases) the corresponding results obtained by recent researchers.