Bulletin of the Korean Mathematical Society (대한수학회보)

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THE THIRD HERMITIAN-TOEPLITZ AND HANKEL DETERMINANTS FOR PARABOLIC STARLIKE FUNCTIONS

  • Rosihan M. Ali (School of Mathematical Sciences Universiti Sains Malaysia) ;
  • Sushil Kumar (Bharati Vidyapeeth's College of Engineering) ;
  • Vaithiyanathan Ravichandran (Department of Mathematics National Institute of Technology)
  • Received : 2021.05.07
  • Accepted : 2023.01.26
  • Published : 2023.03.31
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Abstract

A normalized analytic function f is parabolic starlike if w(z) := zf' (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w - 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

Keywords

Acknowledgement

The authors are deeply appreciative of the referee for the insightful comments. The first author gratefully acknowledges support from a USM research university grant 1001.PMATHS.8011101.

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