<p>Let <i>S</i>(<i>p</i>) represent the collection of meromorphic univalent functions <i>f</i> in the unit disc <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2024_1821_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">D</mi> </math></EquationSource> </InlineEquation> which possess a simple pole at <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2024_1821_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="125" /> </InlineMediaObject> <EquationSource Format="TEX">\(z = p\,(0&lt; p &lt; 1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo>=</mo> <mi>p</mi> <mspace width="0.166667em" /> <mo stretchy="false">(</mo> <mn>0</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and meet the normalization <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2024_1821_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="148" /> </InlineMediaObject> <EquationSource Format="TEX">\(f(0) = f'(0) - 1 = 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <mn>1</mn> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. In this article, we determine bounds for Hermitian Toeplitz determinants whose entries are the Taylor coefficients of functions in <i>S</i>(<i>p</i>). Furthermore, we derive bounds for Hermitian Toeplitz determinants for two specific subclasses of <i>S</i>(<i>p</i>).</p>

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Hermitian Toeplitz Determinant for Certain Meromorphic Univalent Functions

  • Alana John,
  • Firdoshi Parveen

摘要

Let S(p) represent the collection of meromorphic univalent functions f in the unit disc \(\mathbb {D}\) D which possess a simple pole at \(z = p\,(0< p < 1)\) z = p ( 0 < p < 1 ) and meet the normalization \(f(0) = f'(0) - 1 = 0\) f ( 0 ) = f ( 0 ) - 1 = 0 . In this article, we determine bounds for Hermitian Toeplitz determinants whose entries are the Taylor coefficients of functions in S(p). Furthermore, we derive bounds for Hermitian Toeplitz determinants for two specific subclasses of S(p).