Toeplitz Determinants for Inverse of Analytic Functions

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...

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Main Authors: Sarem H. Hadi, Yahea Hashem Saleem, Alina Alb Lupaş, Khalid M. K. Alshammari, Abdullah Alatawi
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/4/676
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author Sarem H. Hadi
Yahea Hashem Saleem
Alina Alb Lupaş
Khalid M. K. Alshammari
Abdullah Alatawi
author_facet Sarem H. Hadi
Yahea Hashem Saleem
Alina Alb Lupaş
Khalid M. K. Alshammari
Abdullah Alatawi
author_sort Sarem H. Hadi
collection DOAJ
description 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.
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issn 2227-7390
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series Mathematics
spelling doaj-art-70e67088c78c4a20b328ae8f21facf282025-08-20T02:01:23ZengMDPI AGMathematics2227-73902025-02-0113467610.3390/math13040676Toeplitz Determinants for Inverse of Analytic FunctionsSarem H. Hadi0Yahea Hashem Saleem1Alina Alb Lupaş2Khalid M. K. Alshammari3Abdullah Alatawi4Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, IraqDepartment of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, IraqDepartment of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, RomaniaDepartment of Mathematics, College of Science, University of Ha’il, Ha’il 55425, Saudi ArabiaDepartment of Scientific and Applied Materials, King Abdullah Air Defence Academy, Taif 26315, Saudi ArabiaEstimates 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.https://www.mdpi.com/2227-7390/13/4/676analytic functionsbi-univalent functionsToeplitz determinants
spellingShingle Sarem H. Hadi
Yahea Hashem Saleem
Alina Alb Lupaş
Khalid M. K. Alshammari
Abdullah Alatawi
Toeplitz Determinants for Inverse of Analytic Functions
Mathematics
analytic functions
bi-univalent functions
Toeplitz determinants
title Toeplitz Determinants for Inverse of Analytic Functions
title_full Toeplitz Determinants for Inverse of Analytic Functions
title_fullStr Toeplitz Determinants for Inverse of Analytic Functions
title_full_unstemmed Toeplitz Determinants for Inverse of Analytic Functions
title_short Toeplitz Determinants for Inverse of Analytic Functions
title_sort toeplitz determinants for inverse of analytic functions
topic analytic functions
bi-univalent functions
Toeplitz determinants
url https://www.mdpi.com/2227-7390/13/4/676
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AT khalidmkalshammari toeplitzdeterminantsforinverseofanalyticfunctions
AT abdullahalatawi toeplitzdeterminantsforinverseofanalyticfunctions