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<p>In this paper, we define subclass <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1269_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="94" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathfrak {D}}_{\Sigma }(\delta ,\beta ,\alpha ,t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="fraktur">D</mi> <mi mathvariant="normal">Σ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>δ</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of the function class <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1269_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Σ</mi> </math></EquationSource> </InlineEquation> of bi-univalent functions defined in the open unit disk in the complex plane. Using Chebyshev polynomials, we have investigated the upper bound for the second Hankel determinant for this function class.</p>

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On the second Hankel determinant of certain subclass of bi-univalent functions

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Waggas Galib Atshan,
  • Ibtihal Abdul Ridha Rahman,
  • Sibel Yalçın

摘要

In this paper, we define subclass \({\mathfrak {D}}_{\Sigma }(\delta ,\beta ,\alpha ,t)\) D Σ ( δ , β , α , t ) of the function class \(\Sigma \) Σ of bi-univalent functions defined in the open unit disk in the complex plane. Using Chebyshev polynomials, we have investigated the upper bound for the second Hankel determinant for this function class.