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<p>In this paper, we establish the sharp bounds of the generalized Toeplitz determinants whose entries are the coefficients of a class of holomorphic functions on the unit disk <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1684_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {U}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">U</mi> </math></EquationSource> </InlineEquation>. Next, we obtain some refinements of the Fekete and Szegö inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space. As some applications, we establish the sharp bounds of the generalized Toeplitz determinants formed over the related terms of homogeneous expansion of a class of holomorphic mappings defined on the unit ball of a complex Banach space. The results presented here would generalize and refine many known results.</p>

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Some Refinements of the Fekete and Szegö Inequalities and Toeplitz Determinants in One and Higher Dimensions

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Zhenyu Xu,
  • Peng He,
  • Qinghua Xu

摘要

In this paper, we establish the sharp bounds of the generalized Toeplitz determinants whose entries are the coefficients of a class of holomorphic functions on the unit disk \(\mathbb {U}\) U . Next, we obtain some refinements of the Fekete and Szegö inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space. As some applications, we establish the sharp bounds of the generalized Toeplitz determinants formed over the related terms of homogeneous expansion of a class of holomorphic mappings defined on the unit ball of a complex Banach space. The results presented here would generalize and refine many known results.