second hankel determinant for certain subclasses of bi-starlike functions defined by differential operators

In this paper, we obtain upper bounds of the initialtaylor-maclaurin coefficients |a2| , |a3| and |a4| and of the feketeszegö 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 havealso 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.