Second Hankel Determinant for Certain Subclasses of Bi-starlike Functions Defined by Differential Operators

In this paper, we obtain upper bounds of the initial Taylor-Maclaurin coefficients |a2| , |a3| and |a4| and of the Fekete Szegö functional [a3 − ηa2^2 ] for certain subclasses of analytic and bi-starlike functions S^∗σ(β, θ, n, m) in the open unit disk. We have also obtained an upper bound of the functional [a2a4−a23] for the functions in the class S^∗σ(β, θ, n, m). Moreover, several interesting applications of the results presented here are also discussed.