JIPAM

Sufficient Conditions for Starlikeness and Convexity in $|z|< 1/2$  
 
  Authors: Mamoru Nunokawa, Shigeyoshi Owa, Yayoi Nakamura, Toshio Hayami,  
  Keywords: Analytic, Starlike, Convex.  
  Date Received: 18/02/08  
  Date Accepted: 04/06/08  
  Subject Codes:

Primary 30C45.

  
  Editors: Anthony Sofo,  
 
  Abstract:

For analytic functions $ f(z)$ with $ f(0) = f^{prime}(0)-1=0$ in the open unit disc $ mathbb{E}$, T. H. MacGregor has considered some conditions for $ f(z)$ to be starlike or convex. The object of the present paper is to discuss some interesting problems for $ f(z)$ to be starlike or convex for $ vert zvert < frac{1}{2}$. ;


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