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Comprehensive subclass of m-fold symmetric bi-univalent functions defined by subordination

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Abstract

In the present paper, we define and investigate the subclass \({{\mathcal {G}}}_{{\Sigma }_m}(\lambda , \tau ,\gamma ,\theta ,\psi )\) of m-fold symmetric bi-univalent functions in the open unit disk \(\textit{U}\) associated with subordination. Moreover, we find estimates on general coefficient \(|a_{mk+1}|\) \(( k \ge 2)\) for functions belong to this subclass \({{\mathcal {G}}}_{{\Sigma }_m}(\lambda , \tau ,\gamma ,\theta ,\psi )\). The results presented in this paper would generalize some related works of several earlier authors.

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Acknowledgements

The authors wish to thank the referees, for the careful reading of the paper and for the helpful suggestions and comments.

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Authors and Affiliations

  1. Faculty of Aviation and Space Sciences, Kocaeli University, Arslanbey Campus, 41285, Kartepe, Kocaeli, Turkey

    Serap Bulut

  2. Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran

    Safa Salehian

  3. Faculty of Mathematical Sciences, Shahrood University of Technology, P.O.Box 316-36155, Shahrood, Iran

    Ahmad Motamednezhad

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  1. Serap Bulut
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  2. Safa Salehian
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  3. Ahmad Motamednezhad
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Correspondence to Safa Salehian.

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Bulut, S., Salehian, S. & Motamednezhad, A. Comprehensive subclass of m-fold symmetric bi-univalent functions defined by subordination. Afr. Mat. 32, 531–541 (2021). https://doi.org/10.1007/s13370-020-00842-w

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