INCLUSION RELATIONS AND RADIUS PROBLEMS FOR A SUBCLASS OF STARLIKE FUNCTIONS

By considering the polynomial function phi(car) (z) = 1 + z + z(2) / 2 , we define the class S-car* consisting of normalized analytic functions f such that z f ' / f is subordinate to phi(car) in the unit disk. The inclusion relations and various radii constants associated with the class S-car* and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.