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Research Article | Open Access

Certain class of bi-univalent functions defined by quantum calculus operator associated with Faber polynomial

Sheza. M. El-Deeb1,2( ), Gangadharan Murugusundaramoorthy3, Kaliyappan Vijaya3, Alhanouf Alburaikan4
Department of Mathematics, College of Science and Arts in Al-Badaya, Qassim University, Buraidah, Saudi Arabia
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, TN, India
Department of Mathematics, College of Science and Arts in Al-Badaya, Qassim University, Buraidah, Saudi Arabia
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Abstract

In this paper, we introduce a new class of bi-univalent functions defined in the open unit disc and connected with a q-convolution. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class by using Faber polynomial expansions, and we obtain an estimation for Fekete-Szegö problem for this class.

Keywords

Faber polynomialbi-univalent functionsconvolutionq-derivative operator
CLC number: 30C45, 30C80

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 2989-3005
DOI: 10.3934/math.2022165

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Cite this article:
El-Deeb SM, Murugusundaramoorthy G, Vijaya K, et al. Certain class of bi-univalent functions defined by quantum calculus operator associated with Faber polynomial. AIMS Mathematics, 2022, 7(2): 2989-3005. https://doi.org/10.3934/math.2022165

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Received: 27 September 2021
Accepted: 15 November 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)