ON THE UNIVALENCE OF CERTAIN POLYHARMONIC MAPPINGS WITH BOUNDED LENGTH DISTORTIONS

  • Xin WANG ,
  • Saminathan PONNUSAMY ,
  • Mingsheng LIU
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  • 1. Department of Mathematics, Shenzhen Polytechnic University, Shenzhen 518055, China;
    2. Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036, India;
    3. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Xin WANG, E-mail: 574149386@qq.com; Saminathan PONNUSAMY, E-mail: samy@iitm.ac.in

Received date: 2023-10-08

  Revised date: 2024-05-05

  Online published: 2024-12-06

Supported by

Liu's research was supported by the Natural Science Foundation of Guangdong Province (2021A1515010058). Wang's research was supported by the Youth Innovation Foundation of Shenzhen Polytechnic University (6024310023K).

Abstract

The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk. We first establish the coefficient estimates for polyharmonic mappings with bounded length distortions. Then, using these results, we establish five Landau-type theorems for subclasses of polyharmonic mappings $F$ and $L(F)$, where $F$ has bounded length distortion and $L$ is a differential operator.

Cite this article

Xin WANG , Saminathan PONNUSAMY , Mingsheng LIU . ON THE UNIVALENCE OF CERTAIN POLYHARMONIC MAPPINGS WITH BOUNDED LENGTH DISTORTIONS[J]. Acta mathematica scientia, Series B, 2024 , 44(6) : 2125 -2138 . DOI: 10.1007/s10473-024-0605-1

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