Coefficients estimate for new subclass of bi-univalent functions associated with quasi-subordination

Abstract

In this paper we introduce and investigate a new subclass of the function class Σ of bi-univalent function defined in the open unit disk, which is associated with the quasi-subordination. We find estimates on the Taylor-MacLaurin coefficient |a2| and |a3| for functions in the defined subclass. Several known and new consequences of these results are also pointed out.