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Starlikeness and Convexity Conditions for Classes of Functions Defined by Subordination  
 
  Authors: R. Aghalary, Jay M. Jahangiri, S.R. Kulkarni,  
  Keywords: Subordination, Hadamard product, Starlike, Convex.  
  Date Received: 21/05/2003  
  Date Accepted: 18/04/2004  
  Subject Codes:

Primary 30C45.

  
  Editors: Herb Silverman,  
 
  Abstract:

We consider the family $ mathcal{P}(1,b), b>0,$ consisting of functions $ p$ analytic in the open unit disc $ U$ with the normalization $ p(0)=1$ which have the disc formulation $ vert p-1vertb$ in $ U.$ Applying the subordination properties to certain choices of $ p$ using the functions $ % f_n(z)=z+sum_{k=1+n}^{infty}a_kz^k, n=1,2,...,$ we obtain inclusion relations, sufficient starlikeness and convexity conditions, and coefficient bounds for functions in these classes. In some cases our results improve the corresponding results appeared in print.;


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