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Properties of New Holomorphic Mappings with Respect to Conic Domains

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Abstract

This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k − ST(α). We introduce new subclasses of starlike (spirallike) functions, namely, S pc (k,α)(S pc (k,α,β)), and discuss their coefficient estimates and the Fekete-Szegö-Goluzin’s problem. Then we generalize S pc (k,α,β) on the unit ball Bn in ℂn, that is, k-conic spirallike mappings of type β and order α. We obtain the growth, covering and distortion theorems of the generalized mappings. Besides that, we construct k-conic spirallike mappings of type β and order α on Bn through Sc(k,α,β) by the generalized Roper-Suffridge extension operators.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, P. R. China

    Yan Yan Cui

  2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, P. R. China

    Yong Hong Xie & Yu Ying Qiao

  3. College of Science, Hebei University of Science and Technology, Shijiazhuang, 050024, P. R. China

    He Ju Yang

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  1. Yan Yan Cui
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  2. Yong Hong Xie
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  4. Yu Ying Qiao
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Correspondence to Yu Ying Qiao.

Additional information

Supported by NSF of China (Grant Nos. 11571089, 11871191), Science and Technology Research Projects of He’nan Provincial Education Department (Grant No. 17A110041) and the key Foundation of Hebei Normal University (Grant No. L2018Z01), Scientific Research Fund of High Level Talents of Zhoukou Normal University (Grant No. ZKNUC2019004)

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Cui, Y.Y., Xie, Y.H., Yang, H.J. et al. Properties of New Holomorphic Mappings with Respect to Conic Domains. Acta. Math. Sin.-English Ser. 37, 971–991 (2021). https://doi.org/10.1007/s10114-021-9380-2

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  • DOI: https://doi.org/10.1007/s10114-021-9380-2

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