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Neighbourhoods and Partial Sums of Starlike Functions Based on Ruscheweyh Derivatives  
 
  Authors: Thomas Rosy, K.G. Subramanian, G. Murugusundaramoorthy,  
  Keywords: Univalent, Starlike, Convex.  
  Date Received: 14/11/02  
  Date Accepted: 26/03/03  
  Subject Codes:

30C45

  
  Editors: Alexandru Lupas (1942-2007),  
 
  Abstract:

In this paper a new class $ S_{p}^{lambda }left( alpha ,beta right) $ of starlike functions is introduced. A subclass $ TS_{p}^{lambda }left( alpha ,beta right) $ of $ S_{p}^{lambda }left( alpha ,beta right) $ with negative coefficients is also considered. These classes are based on Ruscheweyh derivatives. Certain neighbourhood results are obtained. Partial sums $ f_{n}(z)$ of functions $ f(z)$ in these classes are considered and 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)$ are determined.;


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