Hankel determinants, Fekete-Szegö inequality, and estimates of initial coefficients for certain subclasses of analytic functions

Wenzheng Hu; Jian Deng; Wenzheng Hu; Jian Deng

doi:10.3934/math.2024314

AIMS Mathematics

2024, Volume 9, Issue 3: 6445-6467. doi: 10.3934/math.2024314

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Research article

Hankel determinants, Fekete-Szegö inequality, and estimates of initial coefficients for certain subclasses of analytic functions

Wenzheng Hu ,
Jian Deng ^,

School of Mathematical Science, South China Normal University, Guangzhou, 510631, China

Received: 04 December 2023 Revised: 21 January 2024 Accepted: 29 January 2024 Published: 05 February 2024
MSC : 30C45, 30C50

In this paper, we define new subclasses of analytic functions related to a modified sigmoid function and analytic univalent function. Then, we attempt to investigate the upper bounds of the third and fourth Hankel determinant in the special case. Further, bound on third Hankel determinant of its inverse function is also investigated. In addition, we attempt to obtain the Fekete-Szegö inequality for the classes. Then, we estimate the bounds of initial coefficients for the function belongs to some kind of new subclasses when its inverse function also belongs to these new subclasses.
- analytic function,
- modified sigmoid function,
- subordination,
- Hankel determinant,
- upper bound,
- Fekete-Szegöinequality,
- initial coefficients
Citation: Wenzheng Hu, Jian Deng. Hankel determinants, Fekete-Szegö inequality, and estimates of initial coefficients for certain subclasses of analytic functions[J]. AIMS Mathematics, 2024, 9(3): 6445-6467. doi: 10.3934/math.2024314

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Abstract

In this paper, we define new subclasses of analytic functions related to a modified sigmoid function and analytic univalent function. Then, we attempt to investigate the upper bounds of the third and fourth Hankel determinant in the special case. Further, bound on third Hankel determinant of its inverse function is also investigated. In addition, we attempt to obtain the Fekete-Szegö inequality for the classes. Then, we estimate the bounds of initial coefficients for the function belongs to some kind of new subclasses when its inverse function also belongs to these new subclasses.

References

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