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

Sheza. M. El-Deeb; Gangadharan Murugusundaramoorthy; Kaliyappan Vijaya; Alhanouf Alburaikan; Sheza. M. El-Deeb; Gangadharan Murugusundaramoorthy; Kaliyappan Vijaya; Alhanouf Alburaikan

doi:10.3934/math.2022165

AIMS Mathematics

2022, Volume 7, Issue 2: 2989-3005. doi: 10.3934/math.2022165

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

1.
Department of Mathematics, College of Science and Arts in Al-Badaya, Qassim University, Buraidah, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
3.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, TN, India
4.
Department of Mathematics, College of Science and Arts in Al-Badaya, Qassim University, Buraidah, Saudi Arabia

Received: 27 September 2021 Accepted: 15 November 2021 Published: 23 November 2021
MSC : 30C45, 30C80

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.
- Faber polynomial,
- bi-univalent functions,
- convolution,
- $ q $-derivative operator
Citation: Sheza. M. El-Deeb, Gangadharan Murugusundaramoorthy, Kaliyappan Vijaya, Alhanouf Alburaikan. Certain class of bi-univalent functions defined by quantum calculus operator associated with Faber polynomial[J]. AIMS Mathematics, 2022, 7(2): 2989-3005. doi: 10.3934/math.2022165

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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.

References

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