Faber polynomial coefficient estimates of bi-univalent functions connected with the $q$-convolution

Abstract

We introduce a new class of bi-univalent functions defined in the open unit disc and connected with a $q$-convolution. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class by using Faber polynomial expansions and we obtain an estimation for the Fekete-Szegö problem for this class.

Keywords

• faber polynomial
• bi-univalent function
• convolution
• $q$-derivative operator