Certain subclasses of uniformly starlike and convex functions defined by convolution with negative coefficients

M. K. Aouf, A. A. Shamandy, A. O. Mostafa, A. K. Wagdy

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.