"A normalized function $f$ on the open unit disc is starlike (or convex) univalent if associated $zf'(z)/f(z)$ $1+zf''(z)/f'(z)$) a with positive real part. The radius of starlikeness or convexity usually obtained by using estimates for functions Using subordination, we examine various starlikeness, in particular, radii Janowski and order $\beta$, when either convex $(zf'(z)+\alpha z^2f''(z))/f...

In this paper, we define a generalized class of starlike functions with negative coefficients and obtain coefficient estimates, distortion bounds, closure theorems and extreme points. Further we obtain modified Hadamard product, radii of close-to-convex, starlikeness and convexity for functions belonging to this class. Furthermore neighborhood results are discussed.

In the paper we define classes of meromorphic multivalent functions with Montel’s normalization. We investigate the coefficients estimates, distortion properties, the radius of starlikeness, subordination theorems and partial sums for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned.

In the present note, the authors present a criterion for starlikeness of analytic maps satisfying a differential inequality in the open unit disc E = {z : |z| < 1} and claim that their result unifies a number of previously known results in this direction. 2010 Mathematics Subject Classification: Primary 30C80, Secondary 30C45.

T. N. Shanmugam1 and M. P. Jeyaraman2 1 Department of Mathematics, College of Engineering, Anna University, Chennai 600025, India 2 Department of Mathematics, Easwari Engineering College, Chennai 600089, India Correspondence should be addressed to M. P. Jeyaraman, jeyaraman [email protected] Received 27 July 2009; Accepted 8 October 2009 Recommended by Narendra Kumar Govil We apply the general the...