Coefficient estimates of negative powers and inverse coefficients for certain starlike functions

For ?1≤B<A≤1, let (mathcal {S}^{*}(A,B)) denote the class of normalized analytic functions (f(z)= z+{sum }_{n=2}^{infty }a_{n} z^{n}) in |z|<1 which satisfy the subordination relation z f ^′(z)/f(z)?(1 + A z)/(1 + B z) and Σ^?(A,B) be the corresponding class of meromorphic functions in |z|>1. For (fin mathcal {S}^{*}(A,B)) and λ>0, we shall estimate the absolute value of the Taylor coefficients a _n (?λ,f) of the analytic function (f(z)/z)^?λ . Using this we shall determine the coefficient estimate for inverses of functions in the classes (mathcal {S}^{*}(A,B)) and Σ^?(A,B).