Axioms (May 2023)

Coefficient Estimation Utilizing the Faber Polynomial for a Subfamily of Bi-Univalent Functions

  • Abdullah Alsoboh,
  • Ala Amourah,
  • Fethiye Müge Sakar,
  • Osama Ogilat,
  • Gharib Mousa Gharib,
  • Nasser Zomot

DOI
https://doi.org/10.3390/axioms12060512
Journal volume & issue
Vol. 12, no. 6
p. 512

Abstract

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The paper introduces a new family of analytic bi-univalent functions that are injective and possess analytic inverses, by employing a q-analogue of the derivative operator. Moreover, the article establishes the upper bounds of the Taylor–Maclaurin coefficients of these functions, which can aid in approximating the accuracy of approximations using a finite number of terms. The upper bounds are obtained by approximating analytic functions using Faber polynomial expansions. These bounds apply to both the initial few coefficients and all coefficients in the series, making them general and early, respectively.

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