Estimates of coefficients for bi-univalent Ma-Minda-type functions associated with $ \mathfrak{q} $-Srivastava-Attiya operator

Norah Saud Almutairi; Adarey Saud Almutairi; Awatef Shahen; Hanan Darwish; Norah Saud Almutairi; Adarey Saud Almutairi; Awatef Shahen; Hanan Darwish

doi:10.3934/math.2025333

AIMS Mathematics

2025, Volume 10, Issue 3: 7269-7289. doi: 10.3934/math.2025333

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Estimates of coefficients for bi-univalent Ma-Minda-type functions associated with $ \mathfrak{q} $-Srivastava-Attiya operator

1.
Department of Computer Science, College of Engineering and Information Technology, Onaizah Colleges, Qassim 56447, Saudi Arabia
2.
Department of Mathematics, College of Science and Arts, Qassim University, Al Bukairiyah 51941, Al Qassim, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 19 August 2024 Revised: 29 October 2024 Accepted: 04 November 2024 Published: 28 March 2025
MSC : 30C45

In this article, we consider new subclasses of analytic and bi-univalent functions associated with the q-Srivastava-Attiya operator in the open unit disk. We obtain coefficient bounds for the Taylor-Maclaurin coefficients $ |a_2| $ and $ |a_3| $ of the functions of these new subclasses. Furthermore, we establish the Fekete-Szegö inequality for functions in the classes $ \mathcal{T}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\psi), \; \mathcal{KH}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\delta, \psi), \text{and}\; \mathcal{A}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\delta, \psi) $.
- subordination,
- bi-univalent functions,
- $ \mathfrak{q} $-Srivastava-Attiya operator,
- Fekete-Szegö problem
Citation: Norah Saud Almutairi, Adarey Saud Almutairi, Awatef Shahen, Hanan Darwish. Estimates of coefficients for bi-univalent Ma-Minda-type functions associated with $ \mathfrak{q} $-Srivastava-Attiya operator[J]. AIMS Mathematics, 2025, 10(3): 7269-7289. doi: 10.3934/math.2025333

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Abstract

In this article, we consider new subclasses of analytic and bi-univalent functions associated with the q-Srivastava-Attiya operator in the open unit disk. We obtain coefficient bounds for the Taylor-Maclaurin coefficients $ |a_2| $ and $ |a_3| $ of the functions of these new subclasses. Furthermore, we establish the Fekete-Szegö inequality for functions in the classes $ \mathcal{T}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\psi), \; \mathcal{KH}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\delta, \psi), \text{and}\; \mathcal{A}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\delta, \psi) $.

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