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

Abstract

Let S denote the class of analytic and univalent functions in D := {z ∈ C : |z| < 1} of the form f (z) = z + ∞ n=2 a n z n . In this paper, we determine sharp estimates for the Toeplitz determinants whose elements are the Taylor coefficients of functions in S and its certain subclasses. We also discuss similar problems for typically real functions.2010 Mathematics Subject Classification. Primary 30C45, 30C55.

Hankel and Toeplitz Determinants for a Subclass of q-Starlike Functions Associated with a General Conic Domain

“…Corollary 1 (see [25]). If the function f (z) given by (1) belongs to the class S * , then T 3 (2) 84.…”

“…Upon setting Z = (1 − |x| 2 )z and taking the moduli in (25) and using trigonometric inequality, we find that…”

The fourth-order Hermitian Toeplitz determinant for convex functions

“…In recent years a lot of papers has been devoted to the estimation of determinants built with using coefficients of functions in the class A or its subclasses. Hankel matrices i.e., square matrices which have constant entries along the reverse diagonal (see e.g., [3] with further references), and the symmetric Toeplitz determinant (see [1]) are of particular interest.…”

Sharp estimation of Hermitian-Toeplitz determinants for Janowski type starlike and convex functions

“…For more details, we refer the reader to [6,15]. In line of the investigation on Hankel determinants in recent years, Ali et al [1] investigated the sharp bound for the second and third order symmetric Toeplitz determinants. Cudna et al [7] considered the q th -order Hermitian-Toeplitz determinants with its entries as coefficients of the function f (z) given by (1.1) as follows:…”