THE BOHR'S PHENOMENON FOR THE CLASS OF K-QUASICONFORMAL HARMONIC MAPPINGS

doi:10.1007/s10473-026-0215-1

摘要/Abstract

摘要： The primary objective of this paper is to establish several sharp versions of improved Bohr inequality, refined Bohr-type inequality, and refined Bohr-Rogosinski inequality for the class of $K$-quasiconformal sense-preserving harmonic mappings $f=h+\ol{g}$ in the unit disk $\mathbb{D}: = \{z\in\mathbb{C}: |z| < 1\}$. In order to achieve these objectives, we employ the non-negative quantity $S_\rho(h)$ and the concept of replacing the initial coefficients of the majorant series by the absolute values of the analytic function and its derivative, as well as other various settings. Moreover, we obtain the sharp Bohr-Rogosinski radius for harmonic mappings in the unit disk by replacing the bounding condition on the analytic function $h$ with the half-plane condition.

关键词: harmonic mappings, locally univalent functions, Bohr radius, Bohr-Rogosinski radius, improved Bohr radius, refined Bohr radius, $K$-quasiconformal mappings

Abstract: The primary objective of this paper is to establish several sharp versions of improved Bohr inequality, refined Bohr-type inequality, and refined Bohr-Rogosinski inequality for the class of $K$-quasiconformal sense-preserving harmonic mappings $f=h+\bar{g}$ in the unit disk $\mathbb{D}: = \{z\in\mathbb{C}: |z| < 1\}$. In order to achieve these objectives, we employ the non-negative quantity $S_\rho(h)$ and the concept of replacing the initial coefficients of the majorant series by the absolute values of the analytic function and its derivative, as well as other various settings. Moreover, we obtain the sharp Bohr-Rogosinski radius for harmonic mappings in the unit disk by replacing the bounding condition on the analytic function $h$ with the half-plane condition.

Key words: harmonic mappings, locally univalent functions, Bohr radius, Bohr-Rogosinski radius, improved Bohr radius, refined Bohr radius, $K$-quasiconformal mappings

中图分类号:

30A10

Raju BISWAS, Rajib MANDAL. THE BOHR'S PHENOMENON FOR THE CLASS OF K-QUASICONFORMAL HARMONIC MAPPINGS[J]. 数学物理学报(英文版), 2026, 46(2): 790-811.

Raju BISWAS, Rajib MANDAL. THE BOHR'S PHENOMENON FOR THE CLASS OF K-QUASICONFORMAL HARMONIC MAPPINGS[J]. Acta mathematica scientia,Series B, 2026, 46(2): 790-811.

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