Coefficient estimates for a subclass of analytic and bi-univalent functions

Abstract

In the present investigation, we consider a new subclass Σ(τ,γ,φ) of the class Σ consisting of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class Σ(τ,γ,φ) introduced here, we obtain estimates on the first two Taylor–Maclaurin coefficients |a2| and |a3|. Several related classes of analytic and bi-univalent functions in U are also considered and connections to some of the earlier known results are pointed out.