Bohr radius for certain close-to-convex harmonic mappings

2020/12/12 by Molla Basir Ahamed, Vasudevarao Allu, Ahamed, Molla Basir +3
Mathematics · #30C45 #30C50 #30C80 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2012.06829

openalex publication_date 2020/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be the class of harmonic functions f=h+g in the unit disk \mathbbD:=\z∈ℂ : |z|<1\, where h and g are analytic in \mathbbD . Let P_H⁰(α)=\f=h+g ∈ H : \real (h^′(z)-α)gt;|g^′(z)| with 0≤αlt;1, g^′(0)=0, z ∈ \mathbbD\ be the class of close-to-convex mappings defined by Li and Ponnusamy \citeInjectivity section. In this paper, we obtain the sharp Bohr-Rogosinski radius, improved Bohr radius and refined Bohr radius for the class P_H⁰(α) .

Citations

• The Bohr Phenomenon for analytic functions on simply connected domains

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