A Subclass of Bi-univalent Functions Defined by aSymmetric q-Derivative Operator and Gegenbauer Polynomials

Authors

  • Mohamed Illafe School of Engineering, Math, and Technology, Navajo Technical. University, Crownpoint, NM 87313, USA
  • Maisarah Haji Mohd
  • Feras Yousef
  • Shamani Supramaniam

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5408

Keywords:

Bi-univalent analytic functions; , Gegenbauer(or Ultraspherical) polynomials; , Fekete-Szegö functional

Abstract

This paper introduces a novel subclass of bi-univalent analytic functions by utilizing a symmetric q-derivative operator in conjunction with Gegenbauer polynomials. Within this newly defined subclass, we derive bounds for the first two Maclaurin coefficients and address the Fekete-Szeg o problem. By varying the parameters in our results between 0 and 1, we obtain a range of new insights and rediscover some previously established results. This approach not only broadens the scope of bi-univalent function theory but also deepens the understanding of coefficient bounds and extremal problems within this context.

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Published

2024-10-31

Issue

Vol. 17 No. 4: (October 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 Mohamed Illafe, Maisarah Haji Mohd, Feras Yousef, Shamani Supramaniam

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How to Cite

A Subclass of Bi-univalent Functions Defined by aSymmetric q-Derivative Operator and Gegenbauer Polynomials. (2024). European Journal of Pure and Applied Mathematics, 17(4), 2467-2480. https://doi.org/10.29020/nybg.ejpam.v17i4.5408