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On the Fekete-Szegö Problem for Some Subclasses of Analytic Functions  
 
  Authors: T.N. Shanmugam, S. Sivasubramanian,  
  Keywords: Analytic functions, Starlike functions, Subordination, Coefficient problem, Fekete-Szegö inequality
 
  Date Received: 12/05/05  
  Date Accepted: 24/05/05  
  Subject Codes:

Primary 30C45

  
  Editors: Saburou Saitoh,  
 
  Abstract:

In this present investigation, the authors obtain Fekete-Szegö's inequality for certain normalized analytic functions $ f(z)$ defined on the open unit disk for which $ \frac{ z f^{\prime}(z) + \alpha z ^{2} f^{\prime\prime}(z)}{(1-\alpha) f(z)+\alpha z f^{\prime}(z)}$ $ (\alpha \geq 0)$ lies in a region starlike with respect to $ 1$ and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, Fekete-Szegö's inequality for a class of functions defined through fractional derivatives is obtained. The Motivation of this paper is to give a generalization of the Fekete-Szegö inequalities obtained by Srivastava and Mishra .;


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