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Starlikeness associated with the sine hyperbolic function

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Abstract

Let (z) = 1 + λsinh(ς), 0 < λ < 1/sinh(1) be a non-vanishing analytic function in the open unit disk. We introduce a subclass \({{\cal S}^ * }({q_\lambda })\) () of starlike functions which contains the functions \(\mathfrak{f}\) such that \(z{\mathfrak{f}^\prime }/\mathfrak{f}\) is subordinated by . We establish inclusion and radii results for the class \({{\cal S}^ * }\) () for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class \({{\cal S}^ * }\) (). We also find a sharp bound for the third Hankel determinant for the case λ = 1/2.

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Correspondence to Jinlin Liu.

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Conflict of Interest The authors declare no conflict of interest.

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The first author’s work was supported by the Grant No. 20-16367/NRPU/RD/HEC/2021 2021.

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Raza, M., Zahid, H. & Liu, J. Starlikeness associated with the sine hyperbolic function. Acta Math Sci 44, 1244–1270 (2024). https://doi.org/10.1007/s10473-024-0404-8

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  • DOI: https://doi.org/10.1007/s10473-024-0404-8

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