Improved Bohr inequality for harmonic mappings

Gang Liu and Saminathan Ponnusamy

Mathematische Nachrichten, 2023, vol. 296, issue 2, 716-731

Abstract: In order to improve the classical Bohr inequality, we explain some refined versions for a quasi‐subordination family of functions in this paper, one of which is key to build our results. Using these investigations, we establish an improved Bohr inequality with refined Bohr radius under particular conditions for a family of harmonic mappings defined in the unit disk D${\mathbb {D}}$. Along the line of extremal problems concerning the refined Bohr radius, we derive a series of results. Here, the family of harmonic mappings has the form f=h+g¯$f=h+\overline{g}$, where g(0)=0$g(0)=0$, the analytic part h is bounded by 1 and that |g′(z)|≤k|h′(z)|$|g^{\prime }(z)|\le k|h^{\prime }(z)|$ in D${\mathbb {D}}$ and for some k∈[0,1]$k\in [0,1]$.

Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202000408

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:2:p:716-731

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().