The aim of this paper is to obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions belonging to the class $TS(g,\lambda;\alpha,\beta)$. Furthermore partial sums $f_{n}(z)$ of functions $f(z)$ in the class $TS(g,\lambda;\alpha,\beta)$ are considered and sharp lower bounds for the ratios of real part of $f(z)$ to $f_{n}(z)$ and $f'(z)$ to $f_{n}'(z)$ are determined.