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Toeplitz Determinants for Inverse of Analytic Functions

Author

Listed:
  • Sarem H. Hadi

    (Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
    Department of Business Management, Al-Imam University College, Balad 34011, Iraq)

  • Yahea Hashem Saleem

    (Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq)

  • Alina Alb Lupaş

    (Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania)

  • Khalid M. K. Alshammari

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 55425, Saudi Arabia)

  • Abdullah Alatawi

    (Department of Scientific and Applied Materials, King Abdullah Air Defence Academy, Taif 26315, Saudi Arabia)

Abstract

Estimates bounds for Carathéodory functions in the complex domain are applied to demonstrate sharp limits for the inverse of analytic functions. Determining these values is considered a more difficult task compared to finding the values of analytic functions themselves. The challenge lies in finding the sharp estimate for the functionals. While some recent studies have made progress in calculating the sharp boundary values of Hankel determinants associated with inverse functions, the Toeplitz determinant is yet to be addressed. Our research aims to estimate the determinants of the Toeplitz matrix, which is also linked to inverse functions. We also focus on computing these determinants for familiar analytical functions (pre-starlike, starlike, convex, symmetric-starlike) while investigating coefficient values. The study also provides an improvement to the estimation of the determinants of the pre-starlike class presented by Li and Gou.

Suggested Citation

  • Sarem H. Hadi & Yahea Hashem Saleem & Alina Alb Lupaş & Khalid M. K. Alshammari & Abdullah Alatawi, 2025. "Toeplitz Determinants for Inverse of Analytic Functions," Mathematics, MDPI, vol. 13(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:676-:d:1594348
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    References listed on IDEAS

    as
    1. V. Radhika & S. Sivasubramanian & G. Murugusundaramoorthy & Jay M. Jahangiri, 2016. "Toeplitz Matrices Whose Elements Are the Coefficients of Functions with Bounded Boundary Rotation," Journal of Complex Analysis, Hindawi, vol. 2016, pages 1-4, September.
    2. Lei Shi & Hari M. Srivastava & Ayesha Rafiq & Muhammad Arif & Muhammad Ihsan, 2022. "Results on Hankel Determinants for the Inverse of Certain Analytic Functions Subordinated to the Exponential Function," Mathematics, MDPI, vol. 10(19), pages 1-15, September.
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