Coefficient bounds for certain families of bi-Bazilevič and bi-Ozaki-close-to-convex functions

Muajebah Hidan; Abbas Kareem Wanas; Faiz Chaseb Khudher; Gangadharan Murugusundaramoorthy; Mohamed Abdalla; Muajebah Hidan; Abbas Kareem Wanas; Faiz Chaseb Khudher; Gangadharan Murugusundaramoorthy; Mohamed Abdalla

doi:10.3934/math.2024395

AIMS Mathematics

2024, Volume 9, Issue 4: 8134-8147. doi: 10.3934/math.2024395

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Coefficient bounds for certain families of bi-Bazilevič and bi-Ozaki-close-to-convex functions

1.
Mathematics Department, College of Science, King Khalid University, Abha, Saudi Arabia
2.
Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58001, Al-Qadisiyah, Iraq
3.
Department of Mathematics, College of Science, University of Al-Qadisiyah, Al-Qadisiyah, Iraq
4.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology(VIT), Vellore 632014, Tamil Nadu, India
5.
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt

Received: 03 December 2023 Revised: 11 January 2024 Accepted: 06 February 2024 Published: 26 February 2024
MSC : 30C45, 30C50

The aim of this work is to introduce two families, $ \mathcal{B}_{\Sigma}(\wp; \vartheta) $ and $ \mathcal{O}_{\Sigma}(\varkappa; \vartheta) $, of holomorphic and bi-univalent functions involving the Bazilevič functions and the Ozaki-close-to-convex functions, by using generalized telephone numbers. We determinate upper bounds on the Fekete-Szegö type inequalities and the initial Taylor-Maclaurin coefficients for functions in these families. We also highlight certain edge cases and implications for our findings.
- bi-univalent function,
- holormorphic function,
- Bazilevič function,
- Ozaki-close-to-convex functions,
- upper bounds,
- telephone numbers,
- Fekete-Szegö problem
Citation: Muajebah Hidan, Abbas Kareem Wanas, Faiz Chaseb Khudher, Gangadharan Murugusundaramoorthy, Mohamed Abdalla. Coefficient bounds for certain families of bi-Bazilevič and bi-Ozaki-close-to-convex functions[J]. AIMS Mathematics, 2024, 9(4): 8134-8147. doi: 10.3934/math.2024395

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Abstract

The aim of this work is to introduce two families, $ \mathcal{B}_{\Sigma}(\wp; \vartheta) $ and $ \mathcal{O}_{\Sigma}(\varkappa; \vartheta) $, of holomorphic and bi-univalent functions involving the Bazilevič functions and the Ozaki-close-to-convex functions, by using generalized telephone numbers. We determinate upper bounds on the Fekete-Szegö type inequalities and the initial Taylor-Maclaurin coefficients for functions in these families. We also highlight certain edge cases and implications for our findings.

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