Bounds of sixth-order Toeplitz determinant for the families of function associated with bounded turnings

Omar S.  Erzig; Abdul Rahman S.  Juma; Ali  Al-Fayadh

doi:10.24996/ijs.2025.66.11.27

Authors

Omar S. Erzig Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Ramadi, Iraq
Abdul Rahman S. Juma Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad
Ali Al-Fayadh Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad

DOI:

https://doi.org/10.24996/ijs.2025.66.11.27

Keywords:

Toeplitz determinants, Hankel determinants, analytic functions, Bounded Turnings function

Abstract

This research focused on studying the Toeplitz determinants for classes of functions with bounded turnings. Before that, some previous studies of Hankel's determinants have been discussed, due to their strong association with Toplitz determinants. They share most of the mathematical features. For example, if the transpose of both matrices is taken, then the original matrix is obtained. On the other hand, for the set BT of univalent functions with bounded turnings, estimates of the sixth-order Toeplitz determinants have been provided in the unit disc. Besides, the sixth Toeplitz determinant for the and was found, which subfamilies of the family.