Hermitian Toeplitz determinants of the second and third-order for classes of close-to-star functions

Abstract

For some subclasses of close-to-star functions the sharp upper and lower bounds of the second and third-order Hermitian Toeplitz determinants are computed.

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

“…In this paper, we continue this research by computing the sharp upper and lower bounds of the second-and third-order Hermitian Toeplitz determinants over some subclasses of close-to-convex functions, but first noting that the following general result was proved in [11].…”

“…In [9,11,14], research was investigated into the study of Hermitian Toeplitz determinants whose entries are the coefficients of functions in subclasses of A.…”

Sharp Bounds of the Hermitian Toeplitz Determinants for Certain Close-to-Star Functions

“…In [8,10,13], the study to estimate the determinants T q,n ( f ) whose entries are coefficients of functions in subclasses of A was initiated. As it is well known, Hermitian Toeplitz matrices play an important role in functional analysis, applied mathematics and in technical sciences.…”

“…are particularly interesting and were separately studied by various authors. In [10], the sharp bounds of the second-and third-order Hermitian Toeplitz determinants were computed for the classes CST 0 (g 1 ) and CST 0 (g 2 ). In this paper, we will estimate the second-and third-order Hermitian Toeplitz determinants for the other two classes, i.e., for CST 0 (g 3 ) =: F 1 and CST 0 (g 4 ) =: F 2 , in which elements f in view of (1.2) satisfy the condition…”

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].…”