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Abstract <p>The classical result of Bohr and its subsequent generalizations remain active field of study, driving investigations in a wide range of function spaces. In this paper, one of our aims is to study the classical Bohr inequality applicable for certain class of analytic functions on unit disk <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7236_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="163" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{D}:=\left\{z\in\mathbb{C}:|z|&lt;1\right\}\)</EquationSource> <!--ContMath2460200Ahamed-m1--> </InlineEquation>. Moreover, we generalize the Bohr inequality for operator-valued holomorphic functions, <i>i.e.,</i> holomorphic functions from <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7236_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{D}\)</EquationSource> <!--ContMath2460200Ahamed-m2--> </InlineEquation> to <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7236_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{B}(\mathcal{H})\)</EquationSource> <!--ContMath2460200Ahamed-m3--> </InlineEquation>, where <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7236_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{B}(\mathcal{H})\)</EquationSource> <!--ContMath2460200Ahamed-m4--> </InlineEquation> is the set of bounded linear operators on a complex Hilbert space <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7236_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{H}\)</EquationSource> <!--ContMath2460200Ahamed-m5--> </InlineEquation>. Further, we prove Bohr inequality for certain subclasses of harmonic mappings defined on the unit disk <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7236_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{D}\)</EquationSource> <!--ContMath2460200Ahamed-m6--> </InlineEquation>.</p>

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The Bohr Inequality for Certain Classes of Analytic Functions and Its Generalizations

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • M. B. Ahamed,
  • R. Rudrani,
  • R. B. Sharma

摘要

Abstract

The classical result of Bohr and its subsequent generalizations remain active field of study, driving investigations in a wide range of function spaces. In this paper, one of our aims is to study the classical Bohr inequality applicable for certain class of analytic functions on unit disk \(\mathbb{D}:=\left\{z\in\mathbb{C}:|z|<1\right\}\) . Moreover, we generalize the Bohr inequality for operator-valued holomorphic functions, i.e., holomorphic functions from \(\mathbb{D}\) to \(\mathcal{B}(\mathcal{H})\) , where \(\mathcal{B}(\mathcal{H})\) is the set of bounded linear operators on a complex Hilbert space \(\mathcal{H}\) . Further, we prove Bohr inequality for certain subclasses of harmonic mappings defined on the unit disk \(\mathbb{D}\) .