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<p>For <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(a\in (0,1)\)</EquationSource> </InlineEquation>, let <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {H}_0(a)\)</EquationSource> </InlineEquation> denote the class of analytic functions <i>f</i> in the unit disk <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {D}=\{z\in \mathbb {C}: |z|&lt;1\}\)</EquationSource> </InlineEquation> satisfying <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(f(0) =0\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(f'(0)=a\)</EquationSource> </InlineEquation>, and let <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal {B}_0(a)\)</EquationSource> </InlineEquation> be the subclass of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathcal {H}_0(a)\)</EquationSource> </InlineEquation> consisting of functions bounded in modulus by 1. Let <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\mathcal {B}_0(a,1)\)</EquationSource> </InlineEquation> be the subclass of <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\mathcal {B}_0(a)\)</EquationSource> </InlineEquation> of functions having no nonzero zeros. We determine several starlikeness radii for <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\mathcal {B}_0(a,1)\)</EquationSource> </InlineEquation>. Furthermore, we introduce the class <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\Omega ^a:=\{ f\in \mathcal {H}_0(a): |zf'(z)-f(z)|&lt;1/2\}\)</EquationSource> </InlineEquation> and compute various sharp radii of reciprocal starlikeness for functions in the class <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\Omega ^a\)</EquationSource> </InlineEquation>.</p>

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Starlikeness for Bounded Analytic Functions and Reciprocal Starlikeness for a Class Involving a Differential Inequality

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Saravanarasu Madhumitha,
  • Vaithiyanathan Ravichandran

摘要

For \(a\in (0,1)\) , let \(\mathcal {H}_0(a)\) denote the class of analytic functions f in the unit disk \(\mathbb {D}=\{z\in \mathbb {C}: |z|<1\}\) satisfying \(f(0) =0\) and \(f'(0)=a\) , and let \(\mathcal {B}_0(a)\) be the subclass of \(\mathcal {H}_0(a)\) consisting of functions bounded in modulus by 1. Let \(\mathcal {B}_0(a,1)\) be the subclass of \(\mathcal {B}_0(a)\) of functions having no nonzero zeros. We determine several starlikeness radii for \(\mathcal {B}_0(a,1)\) . Furthermore, we introduce the class \(\Omega ^a:=\{ f\in \mathcal {H}_0(a): |zf'(z)-f(z)|<1/2\}\) and compute various sharp radii of reciprocal starlikeness for functions in the class \(\Omega ^a\) .