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Tbilisi Mathematical Journal

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Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions

H. M. Srivastava
  • Corresponding author
  • Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ S. Sivasubramanian
  • Corresponding author
  • Department of Mathematics, University College of Engineering, Anna University (Chennai), Tindivanam 604001, Tamil Nadu, India
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ R. Sivakumar
  • Corresponding author
  • Department of Mathematics, University College of Engineering, Anna University (Chennai), Tindivanam 604001, Tamil Nadu, India
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  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-12-30 | DOI: https://doi.org/10.2478/tmj-2014-0011

Abstract

Let ∑ denote the class of functions

belonging to the normalized analytic function class A in the open unit disk U, which are bi-univalent in U, that is, both the function f and its inverse f-1 are univalent in U. The usual method for computation of the coefficients of the inverse function f-1(z) by means of the relation f-1(f(z))= z is too difficult to apply in the case of m-fold symmetric analytic functions in U. Here, in our present investigation, we aim at overcoming this difficulty by using a general formula to compute the coefficients of f-1(z) in conjunction with the residue calculus. As an application, we introduce two new subclasses of the bi-univalent function class ∑ in which both f(z) and f-1(z) are m-fold symmetric analytic functions with their derivatives in the class P of analytic functions with positive real part in U. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for |am+1| and |a2m+1j|.

Keywords: Analytic function; Univalent functions; Bi-Univalent functions; m-Fold symmetric functions; m-Fold symmetric bi-univalent functions

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About the article

Published Online: 2014-12-30


Citation Information: Tbilisi Mathematical Journal, Volume 7, Issue 2, ISSN (Online) 1512-0139, DOI: https://doi.org/10.2478/tmj-2014-0011.

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