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

Abstract

The aim of this paper is to obtain coefficient estimates, distortiontheorems, 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 $f_n(z)$ offunctions $f(z)$ in the class $TS(g,\lambda ;\alpha ,\beta )$ are consideredand sharp lower bounds for the ratios of real part of $f(z)$ to $f_n(z)$and $f^{\prime }(z)$ to $f_n^{\prime }(z)$ aredetermined.