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Subordination and Superordination Results for $\Phi$-like Functions  
 
  Authors: T.N. Shanmugam, S. Sivasubramanian, Maslina Darus,  
  Keywords: Differential subordination, Differential superordination, Convolution, Subordinant.  
  Date Received: 24/06/06  
  Date Accepted: 29/12/06  
  Subject Codes:

30C45.

  
  Editors: Nak Eun Cho,  
 
  Abstract:

Let $ q_1$ be convex univalent and $ q_2$ be univalent in $ f($ Delta),$ $ $ Phi(0)=0$ and $ $ Phi^{$ prime }(0)=1$. We give some applications of first order differential subordination and superordination to obtain sufficient conditions for the function $ f$ to satisfy

$ displaystyle q_1(z) $ prec $ frac{z(f*g)^{$ prime }(z)}{$ Phi(f*g)(z)}$ prec q_2(z) $
where $ g$ is a fixed function. ;


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