Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 5 (2010), 285 -- 295


 K.G. Subramanian, T.V. Sudharsan, R. Thirumalaisamy and H. Silverman

Abstract. We introduce a class TSpg(α) of analytic functions with negative coefficients defined by convolution with a fixed analytic function g(z)=z+Σn=2bnzn, bn>0,|z|<1. We obtain the coefficient inequality, coefficient estimate, distortion theorem, a convolution result, extreme points and integral representation for functions in the class TSpg(α).

2010 Mathematics Subject Classification: 30C45; 30C50.
Keywords: Analytic functions; Starlike functions; Convolution.

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K.G. Subramanian
T.V. Sudharsan
School of Mathematical sciences, Department of Mathematics,
Universiti Sains Malaysia, SIVET College,
11800 Penang, Malaysia. Chennai 601 302 India.
e-mail: e-mail:

R. Thirumalaisamy H. Silverman
Department of Mathematics, Department of Mathematics,
Government Arts College, College of Charleston,
Chennai 600 035 India. Charleston SC 29424, USA.
e-mail: e-mail: