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<p>For starlike functions associated with a cardioid domain, we provide sharp bounds for the Zalcman functional <i>a</i><sub>2</sub><i>a</i><sub>3</sub><i>-a</i><sub>4</sub> and the second and third Hankel determinants. Our result on the third Hankel determinant gives the negative answer to a conjecture given in [L. Shi et al., A study of third Hankel determinant problem for certain subfamilies of analytic functions involving cardioid domain, <i>Mathematics</i>, 7(5):418, 2019].</p>

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Hankel determinants for starlike functions associated with a cardioid domain

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月26日

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  • Mohsan Raza,
  • Amina Riaz,
  • Paweł Zaprawa

摘要

For starlike functions associated with a cardioid domain, we provide sharp bounds for the Zalcman functional a2a3-a4 and the second and third Hankel determinants. Our result on the third Hankel determinant gives the negative answer to a conjecture given in [L. Shi et al., A study of third Hankel determinant problem for certain subfamilies of analytic functions involving cardioid domain, Mathematics, 7(5):418, 2019].