Coefficient bounds for a family of bi-univalent functions involving telephone numbers

Abstract

In the present paper, we introduce and investigate a new family FΣ(γ, λ, δ; ϑ) of holomorphic and bi-univalent functions by using the generalized telephone numbers which defined in the open unit disk Λ. We find upper bounds for the initial Taylor-Maclaurin coefficients and Fekete-Szeg¨o inequality for functions in this family. We also indicate certain special cases and consequences for our results.