A class of bi-univalent functions subordinate to the $ \beta $-Gregory function with an application

Sarem H. Hadi; Yahea Hashem Saleem; Abdullah Alatawi; Maslina Darus; Alina Alb Lupaş; Sarem H. Hadi; Yahea Hashem Saleem; Abdullah Alatawi; Maslina Darus; Alina Alb Lupaş

doi:10.3934/math.2026492

AIMS Mathematics

2026, Volume 11, Issue 4: 11993-12010. doi: 10.3934/math.2026492

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A class of bi-univalent functions subordinate to the $ \beta $-Gregory function with an application

1.
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
2.
Department of Scientific and Applied Materials, King Abdullah Air Defence Academy, 26315 Taif, Saudi Arabia
3.
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor Darul Ehsan, Malaysia
4.
Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii street, Oradea 410087, Romania

Received: 25 February 2026 Revised: 09 April 2026 Accepted: 10 April 2026 Published: 29 April 2026
MSC : 30C45, 30C50

In this investigation, a generalized form of the Gregory function, called the $ \beta $-Gregory function, is derived. This function includes several well-known analytic functions as special cases. We then consider a new symmetric class of analytic and bi-univalent functions related to the $ \beta $-Gregory function. The geometric and analytic properties of this class are investigated, and inclusion relationships with other known subclasses are established under suitable sufficient conditions. Furthermore, we derive accurate estimates of the coefficients of this class and discuss the associated Fekete-Szegö inequality, showing how the results obtained contribute to generalizing and improving several previous works in bi-univalent functions.
- $ \beta $-Gregory coefficients,
- bi-univalent functions,
- Fekete-Szegöinequality
Citation: Sarem H. Hadi, Yahea Hashem Saleem, Abdullah Alatawi, Maslina Darus, Alina Alb Lupaş. A class of bi-univalent functions subordinate to the $ \beta $-Gregory function with an application[J]. AIMS Mathematics, 2026, 11(4): 11993-12010. doi: 10.3934/math.2026492

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Abstract

In this investigation, a generalized form of the Gregory function, called the $ \beta $-Gregory function, is derived. This function includes several well-known analytic functions as special cases. We then consider a new symmetric class of analytic and bi-univalent functions related to the $ \beta $-Gregory function. The geometric and analytic properties of this class are investigated, and inclusion relationships with other known subclasses are established under suitable sufficient conditions. Furthermore, we derive accurate estimates of the coefficients of this class and discuss the associated Fekete-Szegö inequality, showing how the results obtained contribute to generalizing and improving several previous works in bi-univalent functions.

References

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