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

Estimates on the initial coefficients are obtained for normalized analytic functions ff in the open unit disk with ff and its inverse g=f−1g=f−1 satisfying the conditions that zf′(z)/f(z)zf′(z)/f(z) and zg′(z)/g(z)zg′(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.