JIPAM

Coefficients of Inverse Functions in a Nested Class of Starlike Functions of Positive Order  
 
  Authors: A.K. Mishra, P. Gochhayat,  
  Keywords: Univalent functions, Starlike functions of order $alpha$, Convex functions of order $alpha$, Inverse functions, Coefficient estimates.  
  Date Received: 28/07/05  
  Date Accepted: 10/03/06  
  Subject Codes:

30C45.

  
  Editors: Herb Silverman,  
 
  Abstract:

In the present paper we find the estimates on the $ n^{th}$ coefficients in the Maclaurin's series expansion of the inverse of functions in the class $ sum_{n=2}^{infty}n^delta Big(frac{n-alpha}{1-alpha}Big)vert a_nvertleq 1$. For each $ n$ these estimates are sharp when $ alpha$ is close to $ mathit{zero}$ or $ mathit{one}$ and $ delta$ is close to $ mathit{zero}$. Further for the second, third and fourth coefficients the estimates are sharp for every admissible values of $ alpha$ and $ delta$. ;


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