Let Ω denote the class of functions f (z)= z+ a 2 z 2+ a 3 z 3+⋯ belonging to the normalized
analytic function class A in the open unit disk U= z: z< 1, which are bi-univalent in U, that is,
both the function f and its inverse f− 1 are univalent in U. In this paper, we introduce and
investigate two new subclasses of the function class Ω of bi-univalent functions defined in
the open unit disc U, which are associated with a new differential operator of analytic
functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin …