  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 $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both
subordinate to a starlike 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.
