Hermitian-Toeplitz determinants and some coefficient functionals for the starlike functions

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.