Abstract Given coefficient conditions of analytic in unit disk <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf{D}\)</EquationSource> </InlineEquation>, we obtain the radius of starlike of order <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> and convex of order <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> for Cesàro operator of analytic functions <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> in <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf{D}\)</EquationSource> </InlineEquation>. Furthermore, we consider the Cesàro operator of harmonic functions and give the radius of starlike of order <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> and convex of order <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> for Cesàro operator of harmonic functions <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> in <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3250_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf{D}\)</EquationSource> </InlineEquation>. All results are sharp. DOI 10.1134/S1061920824601484

Radius Constants for Cesàro Operator of Analytic and Harmonic Functions in the Unit Disk

期刊论文
发表日期：

2025年9月29日

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Z.Y. Hu,
H.M. Srivastava,
X.Y. Wang

摘要

Abstract

Given coefficient conditions of analytic in unit disk \(\mathbf{D}\) , we obtain the radius of starlike of order \(\alpha\) and convex of order \(\alpha\) for Cesàro operator of analytic functions \(f\) in \(\mathbf{D}\) . Furthermore, we consider the Cesàro operator of harmonic functions and give the radius of starlike of order \(\alpha\) and convex of order \(\alpha\) for Cesàro operator of harmonic functions \(f\) in \(\mathbf{D}\) . All results are sharp.

DOI 10.1134/S1061920824601484