<p>A normalized analytic function <i>f</i> defined on the unit disk is Ma–Minda starlike (with respect to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2359_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$\varphi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>) if the quantity <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2359_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">$zf'(z)/f(z)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is subordinate to the function <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2359_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$\varphi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>. The radius of starlikeness and parabolic starlikeness of the class <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2359_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {S}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation> of univalent functions on the unit disk are well-known. In this paper, we determine the radii of functions in <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2359_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {S}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation> to belong to several well-known classes of Ma–Minda starlike functions.</p>

Ma–Minda Starlikeness of Univalent Functions

期刊论文
发表日期：

2025年2月8日

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Adam Lecko,
Saravanarasu Madhumitha,
Vaithiyanathan Ravichandran

摘要

A normalized analytic function f defined on the unit disk is Ma–Minda starlike (with respect to $\varphi $ $φ$ ) if the quantity $zf'(z)/f(z)$ $z f^{'} (z) / f (z)$ is subordinate to the function $\varphi $ $φ$ . The radius of starlikeness and parabolic starlikeness of the class $\mathcal {S}$ $S$ of univalent functions on the unit disk are well-known. In this paper, we determine the radii of functions in $\mathcal {S}$ $S$ to belong to several well-known classes of Ma–Minda starlike functions.