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

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