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On Harmonic \({\varvec{\nu }}\)-Bloch and \({\varvec{\nu }}\)-Bloch-Type Mappings

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Abstract

The aim of this paper is twofold. One of them is to introduce the class of harmonic \(\nu \)-Bloch-type mappings as a generalization of harmonic \(\nu \)-Bloch mappings and thereby we generalize some recent results of harmonic 1-Bloch-type mappings investigated recently by Efraimidis et al. (Complex Var Elliptic Equ 62:1081–1092, 2017). The other is to investigate some subordination principles for harmonic Bloch mappings and then establish Bohr’s theorem for these mappings and in a general setting, in some cases.

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Authors and Affiliations

  1. College of Mathematics and Statistics (Hunan Provincial Key Laboratory of Intelligent Information Processing and Application), Hengyang Normal University, Hengyang, 421002, Hunan, People’s Republic of China

    Gang Liu

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India

    Saminthan Ponnusamy

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  1. Gang Liu
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  2. Saminthan Ponnusamy
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Correspondence to Saminthan Ponnusamy.

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Liu, G., Ponnusamy, S. On Harmonic \({\varvec{\nu }}\)-Bloch and \({\varvec{\nu }}\)-Bloch-Type Mappings. Results Math 73, 90 (2018). https://doi.org/10.1007/s00025-018-0853-2

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  • DOI: https://doi.org/10.1007/s00025-018-0853-2

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