Toeplitz Matrices Whose Elements Are the Coefficients of Functions with Bounded Boundary Rotation

Abstract

Let R denote the family of functions f(z)=z+∑n=2∞anzn of bounded boundary rotation so that Ref′(z)>0 in the open unit disk U={z:z<1}. We obtain sharp bounds for Toeplitz determinants whose elements are the coefficients of functions f∈R.

Toeplitz Determinants Whose Elements Are the Coefficients of Analytic and Univalent functions

“…For small values of n and q, estimates of the Toeplitz determinant |T q (n)| for functions in S * and K have been studied in [11]. Similarly, estimates of the Toeplitz determinant |T q (n)| for functions in R have been studied in [8], when n and q are small. Apart from [8] and [11], there appears to be little in the literature concerning estimates of Toeplitz determinants.…”

Toeplitz Determinant for a Subclass of Tilted Starlike Functions with Respect to Conjugate Points

“…In recent years, the studies in a problem of estimating the coefficient bounds for the Toeplitz determinants for the class of univalent functions and its subclasses have been done by some researchers such as Al-Khafaji et al (2020), Ali et al (2018, Radhika et al (2018Radhika et al ( , 2016, Ramachandran and Kavitha (2017), , Srivastava et al (2019), Halim (2016), andZhang et al (2019). However, there was no study of finding estimates for the Toeplitz determinants α δ consisting the functions given by (2).…”

"Upper bounds of Toeplitz determinants for a subclass of alpha-close-to-convex functions"

“…The estimates of the first four Toeplitz determinants are obtained for the class R in [15]. In [13], Sahoo considered the class Rα and obtained the bounds of first four Hankel determinants.…”