Coefficient inequalities for certain starlike and convex functions

In this paper, we consider two Ma-Minda-type subclasses of starlike and convex functions associated with the normalized analytic function phi(Ne)(z) = 1 + z - z3/3 that maps an open unit disk onto the Nephroid shaped bounded domain in the right-half of the complex plane. We investigate convolution and quasi-Hadamard product properties for the functions belonging to such classes. In addition, we compute best possible estimates on third order Hermitian-To eplitz determinant and non-sharp estimates on certain third order Hankel determinants for the starlike functions associated with the interior region of Nephroid.