Faber polynomial coefficient estimates for analytic bi-Bazilevi\v c functions

Jay M. Jahangiri, Samaneh G. Hamidi

A function is said to be bi-univalent in the open unit disk $\Bbb{D}$ if both the function and its inverse are univalent in $\Bbb{D} $. By the same token, a function is said to be bi-Bazilevi\v c in $\Bbb{D}$ if both the function and its inverse are Bazilevi\v c there. The behavior of these types of functions are unpredictable and not much is known about their coefficients. In this paper we use the Faber polynomial expansions to find upper bounds for the coefficients of classes of bi-Bazilevi\v c functions. The coefficients bounds presented in this paper are better than those so far appeared in the literature. The technique used in this paper is also new and we hope that this will trigger further interest in applying our approach to other related problems.