Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations

‎A function is said to be bi-univalent < on > the‎ ‎open unit disk $\mathbb{D}$ if both the function and its inverse are‎ ‎univalent in $\mathbb{D}$‎. ‎Not much is known about the behavior of the‎ ‎classes of bi-univalent functions let alone about their coefficients‎. ‎In‎ ‎this paper we use the Faber polynomial expansions to find coefficient‎ ‎estimates for four well-known classes of bi-univalent functions which are‎ ‎defined by subordinations‎. ‎Both the coefficient bounds and the techniques‎ ‎presented are new and we hope that this paper will inspire future‎ ‎researchers in applying our approach to other related problems‎.