Sharp estimate for starlikeness related to a tangent domain

Mohammad Faisal Khan; Jongsuk Ro; Muhammad Ghaffar Khan; Mohammad Faisal Khan; Jongsuk Ro; Muhammad Ghaffar Khan

doi:10.3934/math.20241007

AIMS Mathematics

2024, Volume 9, Issue 8: 20721-20741. doi: 10.3934/math.20241007

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Research article

Sharp estimate for starlikeness related to a tangent domain

1.
Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh-11673, Saudi Arabia
2.
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
3.
Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
4.
Institute of Numerical Science Kohat University of Science and Technology, Kohat, Pakistan

Received: 18 February 2024 Revised: 07 June 2024 Accepted: 13 June 2024 Published: 26 June 2024
MSC : 05A30, 11B65, 30C45, 47B38

In the recent years, the study of the Hankel determinant problems have been widely investigated by many researchers. We were essentially motivated by the recent research going on with the Hankel determinant and other coefficient bounds problems. In this research article, we first considered the subclass of analytic starlike functions connected with the domain of the tangent function. We then derived the initial four sharp coefficient bounds, the sharp Fekete-Szegö inequality, and the sharp second and third order Hankel determinant for the defined class. Also, we derived sharp estimates like sharp coefficient bounds, Fekete-Szegö estimate, and sharp second order Hankel determinant for the functions having logarithmic coefficient and for the inverse coefficient, respectively, for the defined functions class.
- holomorphic functions,
- tangent function,
- inverse coefficient,
- logarithmic coefficients
Citation: Mohammad Faisal Khan, Jongsuk Ro, Muhammad Ghaffar Khan. Sharp estimate for starlikeness related to a tangent domain[J]. AIMS Mathematics, 2024, 9(8): 20721-20741. doi: 10.3934/math.20241007

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Abstract

In the recent years, the study of the Hankel determinant problems have been widely investigated by many researchers. We were essentially motivated by the recent research going on with the Hankel determinant and other coefficient bounds problems. In this research article, we first considered the subclass of analytic starlike functions connected with the domain of the tangent function. We then derived the initial four sharp coefficient bounds, the sharp Fekete-Szegö inequality, and the sharp second and third order Hankel determinant for the defined class. Also, we derived sharp estimates like sharp coefficient bounds, Fekete-Szegö estimate, and sharp second order Hankel determinant for the functions having logarithmic coefficient and for the inverse coefficient, respectively, for the defined functions class.

References

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