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<p>In recent years, researchers have extensively investigated the Hankel determinant, which consists of coefficients appearing in a holomorphic function’s Taylor-Maclaurin series. Hankel matrices are widely used in Markov processes, non-stationary signals, and other mathematical disciplines. The aim of the current research article is to first improve the bounds of coefficient-related problems by employing the well-known Carathéodory function. The problems that we are going to improve were obtained by Tang et al. The sharp estimates of the most difficult problem of geometric function theory known as the third-order Hankel determinant are also contributed here. Zalcman and Fekete-Szegö inequalities are also studied here for the defined family of holomorphic functions.</p>

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Improvement on Hankel determinant bounds for specific holomorphic functions

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Huo Tang,
  • Muhammad Abbas,
  • Reem K. Alhefthi,
  • Muhammad Arif

摘要

In recent years, researchers have extensively investigated the Hankel determinant, which consists of coefficients appearing in a holomorphic function’s Taylor-Maclaurin series. Hankel matrices are widely used in Markov processes, non-stationary signals, and other mathematical disciplines. The aim of the current research article is to first improve the bounds of coefficient-related problems by employing the well-known Carathéodory function. The problems that we are going to improve were obtained by Tang et al. The sharp estimates of the most difficult problem of geometric function theory known as the third-order Hankel determinant are also contributed here. Zalcman and Fekete-Szegö inequalities are also studied here for the defined family of holomorphic functions.