JIPAM

Fekete-Szegö Functional for some Subclass of Non-Bazilevic Functions  
 
  Authors: T.N. Shanmugam, M.P. Jeyaraman, S. Sivasubramanian,  
  Keywords: Analytic functions, Starlike functions, Subordination, Coefficient problem, Fekete-Szegö inequality.  
  Date Received: 18/11/05  
  Date Accepted: 24/03/06  
  Subject Codes:

Primary 30C45.

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

In this present investigation, the authors obtain a sharp Fekete-Szegö's inequality for certain normalized analytic functions $ f(z)$ defined on the open unit disk for which $ (1+ beta)left( frac{z}{f(z)}right)^{alpha}- beta f^{prime}(z) left( frac{z}{f(z)}right)^{1+alpha}, $ $ ( beta in mathbb{C}, 0 < alpha < 1 )$ lies in a region starlike with respect to $ 1$ and is symmetric with respect to the real axis. Also, certain applications of our results 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 also obtained.;


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