Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f − 1 satisfying the conditions that z f ′ ( z ) / f ( z ) and z g ′ ( z ) / g ( z ) are both subordinate to a univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.