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Coefficient Estimates for Certain Classes of Bi-Univalent Functions

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  • Jay M. Jahangiri
  • Samaneh G. Hamidi

Abstract

A function analytic in the open unit disk is said to be bi-univalent in if both the function and its inverse map are univalent there. The bi-univalency condition imposed on the functions analytic in makes the behavior of their coefficients unpredictable. Not much is known about the behavior of the higher order coefficients of classes of bi-univalent functions. We use Faber polynomial expansions of bi-univalent functions to obtain estimates for their general coefficients subject to certain gap series as well as providing bounds for early coefficients of such functions.

Suggested Citation

  • Jay M. Jahangiri & Samaneh G. Hamidi, 2013. "Coefficient Estimates for Certain Classes of Bi-Univalent Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-4, August.
    • Handle: RePEc:hin:jijmms:190560
    DOI: 10.1155/2013/190560
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    References listed on IDEAS

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    1. Samaneh G. Hamidi & Suzeini Abd Halim & Jay M. Jahangiri, 2013. "Faber Polynomial Coefficient Estimates for Meromorphic Bi-Starlike Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-4, March.
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    Cited by:

    1. Şahsene Altınkaya & Sibel Yalçın, 2015. "Coefficient Bounds for Certain Subclasses of -Fold Symmetric Biunivalent Functions," Journal of Mathematics, Hindawi, vol. 2015, pages 1-5, November.
    2. Deborah Olufunmilayo Makinde, 2019. "Coefficient Estimates for Generalized Analytic Bi-Univalent Functions," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 5(12), pages 174-178, 12-2019.

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    2. Jay M. Jahangiri & Samaneh G. Hamidi, 2015. "Faber Polynomial Coefficients of Classes of Meromorphic Bistarlike Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-5, October.
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