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Bohr–Rogosinski Phenomenon for \(\mathcal {S}^*(\psi )\) and \(\mathcal {C}(\psi )\)

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Abstract

In Geometric function theory, occasionally, attempts have been made to solve a particular problem for the Ma-Minda classes, \(\mathcal {S}^*(\psi )\) and \(\mathcal {C}(\psi )\) of univalent starlike and convex functions, respectively. Recently, a popular radius problem generally known as Bohr’s phenomenon has been studied in various settings; however, a little is known about Rogosinski radius. In this article, for a fixed \(f\in \mathcal {S}^*(\psi )\) or \(\mathcal {C}(\psi ),\) the class of analytic subordinants \(S_{f}(\psi ):= \{g : g\prec f \} \) is studied for the Bohr–Rogosinski phenomenon in a general setting. Its applications to the classes \(\mathcal {S}^*(\psi )\) and \(\mathcal {C}(\psi )\) are also shown.

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Acknowledgements

We would like to thank the Editor and the Reviewers for their valuable suggestions to improve this manuscript.

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

    Kamaljeet Gangania & S. Sivaprasad Kumar

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  1. Kamaljeet Gangania
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K. Gangania would like to thank University Grant Commission, New-Delhi, India for providing Junior Research Fellowship under UGC-Ref. No.:1051/(CSIR-UGC NET JUNE 2017)

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Gangania, K., Kumar, S.S. Bohr–Rogosinski Phenomenon for \(\mathcal {S}^*(\psi )\) and \(\mathcal {C}(\psi )\). Mediterr. J. Math. 19, 161 (2022). https://doi.org/10.1007/s00009-022-02074-7

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