Sharp Bounds of the Hermitian Toeplitz Determinants for Some Classes of Close-to-Convex Functions

Abstract

Sharp upper and lower bounds of the Hermitian Toeplitz determinants of the second and third orders are found for various subclasses of close-to-convex functions.

Hermitian-Toeplitz determinants for certain univalent functions

“…In the following corollary, bounds are given for certain classes when coefficients B 1 and B 2 of ϕ(z) satisfy the condition (2.5) or (2.6). Recently, the lower and upper bounds of det T 2,1 (f ) and det T 3,1 (f ) for functions f in F 1 , F 2 , F 3 and F 4 are obtained [11,12,19]. By generalizing these works, when f ∈ K, we obtain the bounds of det T 2,1 (f ) and det T 3,1 (f ) for different choices of g ∈ S * .…”

“…Kowalczyk et al [11] also attained the bounds for the classes F 2 and F 3 . For more work in this direction one can see [1,2,3,18,19].…”

Some properties of certain close-to-convex harmonic mappings

“…In recent years, the Toeplitz determinants and Hankel determinants of functions in the class S or its subclasses have attracted many researchers' attention (see [11,16,18,19,27,28,[31][32][33][34]). Among them, the symmetric Toeplitz determinant |T q (n)| estimates for subclasses of S with small values of n and q, are investigated by [2,7,10,45,52,53].…”