Summary: A subclass \(T^*_n(\alpha,\beta,\gamma)\) consisting of functions of the form \(f(z)=z\sum_{k=2}^\infty a_kz^k\), \(a_k\geq 0\) are considered. The subclass \(T^*_n(\alpha,\beta,\gamma,z_0)\) for which \(f(z_0)=z_0\) or \(f'(z_0)=1\), \(z_0\) real, is examined. The coefficient estimates, distortion theorem, radius of convexity and closure property are obtained for this class.