Hermitian-Toeplitz Determinants for Certain Classes 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 * .…”

“…Obradović and Tuneski [21] derived the bounds for the class S and some of its subclasses. Recently, Kumar [12] obtained the sharp lower and upper bound of det T 2,1 (f ) and det T 3,1 (f ) for the classes F 1 , F 2 , F 3 and F 4 . Kowalczyk et al [11] also attained the bounds for the classes F 2 and F 3 .…”

Hermitian–Toeplitz determinants for functions with bounded turning

“…Kumar et al [22] gave a generalisation to the results investigated in [12] by investigating those results for Janowski starlike and convex functions. Kumar [20] investigated lower and upper bounds on the second and third order Hermitian-Toeplitz determinants for certain subclasses of close-to-convex functions. Some more results in this direction may be found in [10,21].…”

“…The paper [6] gives the higher-order asymptotic formulas for the eigenvalues of large Hermitian-Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the real line and related applications in physics. The determinant of Hermitian-Toeplitz matrices finds its applications in signal processing [29], see also [20].…”