Abstract
Suppose w is a sense-preserving harmonic mapping of the unit disk \({\mathbb D}\) such that \(w({\mathbb D})\subseteq {\mathbb D}\) and w has a zero of order \(p\ge 1\) at \(z=0\). In this paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of \({\mathbb D}\), we further generalize this result.
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We would like to thank the anonymous referees for their helpful comments to improve this paper.
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The research of the authors was supported by NNSF of China Grant Nos. 11501220, 11471128, 11971124, 11971182 NNSF of Fujian Province Grant Nos. 2016J01020, 2019J0101 Subsidized Project for Postgraduates’Innovative Fund in Scientific Research of Huaqiao University and the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-PY402).
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Communicated by Alexander Yu. Solynin.
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Bai, XJ., Huang, J. & Zhu, JF. Boundary Schwarz Lemma for Harmonic Mappings Having Zero of Order p. Bull. Malays. Math. Sci. Soc. 44, 827–838 (2021). https://doi.org/10.1007/s40840-020-00980-1
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DOI: https://doi.org/10.1007/s40840-020-00980-1