Toeplitz Determinants for Inverse of Analytic Functions

Sarem H. Hadi (), Yahea Hashem Saleem, Alina Alb Lupaş (), Khalid M. K. Alshammari and Abdullah Alatawi ()
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Sarem H. Hadi: Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, 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

Mathematics, 2025, vol. 13, issue 4, 1-12

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.

Keywords: analytic functions; bi-univalent functions; Toeplitz determinants (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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