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Loewner Chain Associated with the Modified Roper–Suffridge Extension Operator

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Abstract

In this paper, we will determine under what condition the modified Roper–Suffridge extension operators F and \(\Psi _{n,\frac{1}{p_2},\ldots ,\frac{1}{p_n}}(f)\) can be embedded in a Loewner chain on the unit ball \(B^n\) and on a special bounded convex circular domain \(\Omega _{n,p_2,\ldots ,p_n}\), respectively. In particular, some well-known results can be obtained using the main theorems in this paper.

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Acknowledgments

The authors cordially thank the referees for their reviewing and useful suggestions and comments. This work was supported by the Doctoral Foundation of Pingdingshan University (PXY-BSQD-2015005), the Science Foundation of Zhejiang Province (Y14A010047).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Pingdingshan University, Pingdingshan, 467000, China

    Xiaofei Zhang & Yongjie Li

  2. Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, 475004, China

    Shuxia Feng

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  1. Xiaofei Zhang
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  2. Shuxia Feng
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  3. Yongjie Li
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Correspondence to Xiaofei Zhang.

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Communicated by Filippo Bracci.

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Zhang, X., Feng, S. & Li, Y. Loewner Chain Associated with the Modified Roper–Suffridge Extension Operator. Comput. Methods Funct. Theory 16, 265–281 (2016). https://doi.org/10.1007/s40315-015-0141-z

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  • DOI: https://doi.org/10.1007/s40315-015-0141-z

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