On Harmonic $\nu$-Bloch and $\nu$-Bloch-type mappings

Gang Liu; Saminathan Ponnusamy

On Harmonic $\nu$-Bloch and $\nu$-Bloch-type mappings

Complex Variables 2017-07-07 v1

Authors: Gang Liu , Saminathan Ponnusamy

Abstract

The aim of this paper is twofold. One 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. \cite{EGHV}. 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.

Keywords

harmonic maps bohr phenomenon harmonic functions

Cite

@article{arxiv.1707.01570,
  title  = {On Harmonic $\nu$-Bloch and $\nu$-Bloch-type mappings},
  author = {Gang Liu and Saminathan Ponnusamy},
  journal= {arXiv preprint arXiv:1707.01570},
  year   = {2017}
}

Comments

17 pages; Comments are welcome

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