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

Authors: SARBESWAR BARIK

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.

Keywords: Analytic function, analytic continuation, univalent functions, biunivalent functions, coefficient bounds

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