Faber polynomial coefficients for certain subclasses of analytic and biunivalent functions

Abstract

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions definedin the open unit disc. We use the Faber polynomial expansions to find upper bounds for the nth (n ≥ 3) TaylorMaclaurin coefficients |$a_n$| of functions belong to these new subclasses with $a_k$ = 0 for 2 ≤ k ≤ n − 1, also we findnon-sharp estimates on the first two coefficients |$a_2$| and |$a_3$|. The results, which are presented in this paper, wouldgeneralize those in related earlier works of several authors.