Coefficient estimation of a certain subclass of bi-close-to-convex functions analytic in the exterior of the unit disc

Abstract

In this paper, we introduce two new subclasses of biunivalent functions analytic in the exterior of the unit disc. The bounds obtained for the $zero^{th}$, first and second coefficient improves upon earlier known results. The results are obtained by refining the well-known estimates for the initial coefficients of the Carth$\acute{e}$odory functions.