Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials

Abdulmtalb Hussen; Mohammed S. A. Madi; Abobaker M. M. Abominjil; Abdulmtalb Hussen; Mohammed S. A. Madi; Abobaker M. M. Abominjil

doi:10.3934/math.2024879

AIMS Mathematics

2024, Volume 9, Issue 7: 18034-18047. doi: 10.3934/math.2024879

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Research article

Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials

1.
School of Engineering, Math, & Technology, Navajo Technical University, Crownpoint, NM 87313
2.
Mathematics Department, College of Education, University of Gharyan, Gharyan City, Libya

Received: 20 December 2023 Revised: 13 April 2024 Accepted: 26 April 2024 Published: 28 May 2024
MSC : 30C45

In this paper, we introduced two novel subclasses of bi-univalent functions, $ \mathcal{M}_{\Sigma}(\alpha, \mathcal{B}(x, \xi)) $ and $ \mathcal{H}_{\Sigma}(\alpha, \mu, \mathcal{B}(x, \xi)) $, utilizing Lucas-Balancing polynomials. Within these function classes, we established bounds for the Taylor-Maclaurin coefficients $ \left|a_2\right| $ and $ \left|a_3\right| $, addressing the Fekete-Szegö functional problems specific to functions within these new subclasses. Moreover, we illustrated how our primary findings could lead to various new outcomes through parameter specialization.
- balancing polynomial,
- Lucas-Balancing polynomials,
- bi-univalent functions,
- analytic functions,
- Taylor-Maclaurin coefficients,
- Fekete-Szegö functional
Citation: Abdulmtalb Hussen, Mohammed S. A. Madi, Abobaker M. M. Abominjil. Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials[J]. AIMS Mathematics, 2024, 9(7): 18034-18047. doi: 10.3934/math.2024879

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Abstract

In this paper, we introduced two novel subclasses of bi-univalent functions, $ \mathcal{M}_{\Sigma}(\alpha, \mathcal{B}(x, \xi)) $ and $ \mathcal{H}_{\Sigma}(\alpha, \mu, \mathcal{B}(x, \xi)) $, utilizing Lucas-Balancing polynomials. Within these function classes, we established bounds for the Taylor-Maclaurin coefficients $ \left|a_2\right| $ and $ \left|a_3\right| $, addressing the Fekete-Szegö functional problems specific to functions within these new subclasses. Moreover, we illustrated how our primary findings could lead to various new outcomes through parameter specialization.

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