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On a subfamily of starlike functions related to hyperbolic cosine function

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Abstract

We introduce and study a new Ma–Minda subclass of starlike functions \({\mathcal {S}}^*_{\varrho },\) defined as

$$\begin{aligned} {\mathcal {S}}^{*}_{\varrho }:=\left\{ f\in {\mathcal {A}}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho (z), z\in {\mathbb {D}} \right\} , \end{aligned}$$

associated with an analytic univalent function \(\cosh \sqrt{z},\) where we choose the branch of the square root function so that \(\cosh \sqrt{z}=1+z/2!+z^{2}/{4!}+\cdots .\) We establish certain inclusion relations for \({\mathcal {S}}^{*}_{\varrho }\) and deduce sharp \({\mathcal {S}}^{*}_{\varrho }\)-radii for certain subclasses of analytic functions.

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Acknowledgements

The authors acknowledged the support of Delhi Technological University, Delhi, India, for giving monetary help to complete this research work.

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  1. S. Sivaprasad Kumar contributed equally to this work.

Authors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, Shahbad Daulatpur, Delhi, 110042, India

    Mridula Mundalia & S. Sivaprasad Kumar

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  1. Mridula Mundalia
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  2. S. Sivaprasad Kumar
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Both the authors have equal contribution. Authors are thankful to the reviewers for their valuable suggestions.

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Correspondence to S. Sivaprasad Kumar.

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Communicated by S. Ponnusamy.

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Mundalia, M., Kumar, S.S. On a subfamily of starlike functions related to hyperbolic cosine function. J Anal 31, 2043–2062 (2023). https://doi.org/10.1007/s41478-023-00550-1

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