On coefficient inequalities for certain subclasses of meromorphic bi-univalent functions

Abstract

In the present paper, we investigate and define two subclasses of meromorphic bi-univalent function class Σ′ which are defined on the domain \(\mathbb{U}\)^∗ = {z ∈ \(\mathbb{C}\) : 1 < |z| < \(\infty\)}.  Further, by using the well-known coefficients estimates of the Caratéodory ´functions (i.e functions with positive real part) we obtain the estimates on the coefficients |b₀|, |b₁| and |b₂ + b\(_{0}^{3}\)| for functions in these subclasses.