Bohr Phenomenon for Locally Univalent Functions and Logarithmic Power Series

Abstract

In this article we prove Bohr inequalities for sense-preserving Kquasiconformal harmonic mappings defined in D and obtain the corresponding results for sense-preserving harmonic mappings by letting K → ∞. One of the results includes the sharpened version of a theorem by Kayumov et. al. (Math. Nachr., 291 (2018), no. 11-12, 1757-1768. In addition Bohr inequalities have been established for uniformly locally univalent holomorphic functions, and for log(f (z)/z) where f is univalent or inverse of a univalent function.2010 Mathematics Subject Classification. 30B10, 30C60, 31A05, 30C45.

A generalization of the Bohr-Rogosinski sum

“…Bohr type inequalities for certain integral operators have been obtained in [18,25]. To find certain recent results, we refer to [3,4,12,23,28,30,31] and the references therein. The recent survey article [5] and references therein may be good sources for this topic.…”

Generalization of Bohr-type inequality in analytic functions

“…[1,28,35] and the references therein). Kayumov et al [18,20] considered the problem of determining Bohr radius for the classes of odd analytic functions, and for locally univalent functions, and for derivatives of analytic functions, we refer to [7,8]. Recently, it has become very common to apply Bohr radius to harmonic function [14,19,22] and the Bohr radius of harmonic functions is almost parallel to that of the case of analytic functions.…”

A generalization of the Bohr inequality for bounded analytic functions on simply connected domains and its applications

“…For background information about this inequality and further work related to Bohr's radius, we refer survey article [5] and references therein. Moreover, to find certain recent results, we refer to [3,4,12,22,26,28,30,31]. Many interesting extensions of Bohr's inequality in various settings have been developed by several mathematicians.…”