Abstract
In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the nth (n >= 3) Taylor-Maclaurin coefficients vertical bar a(n)vertical bar of functions belong to these new subclasses with a(k) = 0 for 2 <= k <= n - 1, also we find non-sharp estimates on the first two coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar. The results, which are presented in this paper, would generalize those in related earlier works of several authors.