Applications of Mathematics, Vol. 68, No. 3, pp. 289-304, 2023
Hermitian-Toeplitz determinants and some coefficient functionals for the starlike functions
Deepak Kumar, Virendra Kumar, Laxminarayan Das
Received April 24, 2022. Published online October 18, 2022.
Abstract: In this paper, we have determined the sharp lower and upper bounds on the fourth-order Hermitian-Toeplitz determinant for starlike functions with real coefficients. We also obtained the sharp bounds on the Hermitian-Toeplitz determinants of inverse and logarithmic coefficients for starlike functions with complex coefficients. Sharp bounds on the modulus of differences and difference of moduli of logarithmic and inverse coefficients are obtained. In our investigation, it has been found that the bound on the third-order Hermitian-Toeplitz determinant for starlike functions and its inverse coefficients is invariant.
Affiliations: Deepak Kumar, Department of Applied Mathematics, Delhi Technological University, Delhi 110042, India, e-mail: email@example.com; Virendra Kumar (corresponding author), Department of Mathematics, Ramanujan College, University of Delhi, Kalkaji, Delhi, 110019, India, e-mail: firstname.lastname@example.org; Laxminarayan Das, Department of Applied Mathematics, Delhi Technological University, Delhi 110042, India, e-mail: email@example.com