Improved Bohr's inequality for locally univalent harmonic mappings

Stavros Evdoridis, Saminathan Ponnusamy*, Antti Rasila

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We prove several improved versions of Bohr's inequality for the harmonic mappings of the form [Formula presented], where h is bounded by 1 and |g(z)|≤|h(z)|. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk [Formula presented] under the mapping f is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.

Original languageEnglish
Pages (from-to)201-213
Number of pages13
JournalIndagationes Mathematicae
Volume30
Issue number1
DOIs
StatePublished - Jan 2019

Keywords

  • Bounded analytic functions
  • Harmonic functions
  • Locally univalent functions and Bohr radius

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