| Certain subclasses of uniformly starlike and convex functions defined by convolution with negative coefficients |
| M.K. Aouf, A.A. Shamandy, A.O. Mostafa and A.K. Wagdy |
Abstract 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.
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Keywords: Analytic function; Hadamard product; distortion theorems; partial sums. |
MSC: 30C45 |
Pages: 14$-$28 |
Volume 65 , Issue 1 , 2013 |
