Coefficient Bounds for a Family of Analytic Functions Linked with a Petal-Shaped Domain and Applications to Borel Distribution

Panigrahi, Trailokya; Murugusundaramoorthy, Gangadharan; Pattnayak, Eureka

doi:10.22130/scma.2022.557374.1143

Document Type : Research Paper

Authors

¹ Institute of Mathematics and Applications, Andharua, Bhubaneswar-751029, Odisha, India.

² School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, Tamilnadu, India.

https://doi.org/10.22130/scma.2022.557374.1143

Abstract

In this paper, by employing sine hyperbolic inverse functions, we introduced the generalized subfamily $\mathcal{RK}_{\sinh}(\beta)$ of analytic functions defined on the open unit disk $\Delta:=\{\xi: \xi \in \mathbb{C} \text{ and } |\xi|<1 \}$ associated with the petal-shaped domain. The bounds of the first three Taylor-Maclaurin's coefficients, Fekete-Szeg\"{o} functional and the second Hankel determinants are investigated for $f\in\mathcal{RK}_{\sinh}(\beta)$. We considered Borel distribution as an application to our main results. Consequently, a number of corollaries have been made based on our results, generalizing previous studies in this direction.

Keywords

20.1001.1.23225807.2023.20.3.3.9

Main Subjects

Complex Analysis

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Sahand Communications in Mathematical Analysis

Coefficient Bounds for a Family of Analytic Functions Linked with a Petal-Shaped Domain and Applications to Borel Distribution

References

References

Volume 20, Issue 3
April 2023
Pages 33-50

Coefficient Bounds for a Family of Analytic Functions Linked with a Petal-Shaped Domain and Applications to Borel Distribution

References

References

Volume 20, Issue 3April 2023Pages 33-50

Volume 20, Issue 3
April 2023
Pages 33-50