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<p>In this paper, we obtain some refinements of the Fekete and Szegö inequalities for the normalized biholomorphic mappings which can be embedded as the first element of a <i>g</i>-Loewner chain on the unit disc <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {U}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">U</mi> </math></EquationSource> </InlineEquation> in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation> and on the unit ball <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {B}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">B</mi> </math></EquationSource> </InlineEquation> of a complex Banach space. As an application, we also establish some refinements of the Fekete and Szegö inequality for the images of the first elements of <i>g</i>-Loewner chains on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {U}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">U</mi> </math></EquationSource> </InlineEquation> under the Roper-Suffridge type extension operators on general domains. The results presented here would generalize those given by Hamada et al. (J. Math. Anal. Appl., 2022, 516 (2): 126526).</p>

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Fekete-Szegö Problem for Biholomorphic Mappings which have the Parametric Representation

  • 期刊论文

  • 发表日期：

    2026年5月15日

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  • Zhenyu Xu

摘要

In this paper, we obtain some refinements of the Fekete and Szegö inequalities for the normalized biholomorphic mappings which can be embedded as the first element of a g-Loewner chain on the unit disc \(\mathbb {U}\) U in \(\mathbb {C}\) C and on the unit ball \(\mathbb {B}\) B of a complex Banach space. As an application, we also establish some refinements of the Fekete and Szegö inequality for the images of the first elements of g-Loewner chains on \(\mathbb {U}\) U under the Roper-Suffridge type extension operators on general domains. The results presented here would generalize those given by Hamada et al. (J. Math. Anal. Appl., 2022, 516 (2): 126526).