Toeplitz Determinants Associated with Ma-Minda Classes of Starlike and Convex Functions

Hermitian-Toeplitz determinants for certain univalent functions

“…(see [1]). It is clear that, the lower and the upper estimates of det T 2,1 (f ) will be deduced directly from the bound of |a 2 |, which are sharp for the functions f 1 (z) and f 2 (z) respectively, given by…”

“…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].…”

“…where n, q ∈ N and a 1 = 1. In particular, for functions in starlike and convex classes, T 2 (2)[f ], T 3 (1)[f ] and T 3 (2)[f ] were studied by Ali et al [7]. Sun et al [47] investigated the upper bounds of the third Hankel determinants for the subclass M(α, 1, 1) of closeto-convex harmonic mappings.…”

“…2 t 2n (K (t))2 dt, and L(ζ, n, 1) is defined as in Proposition 4.1.Proof. Let f ∈ HC(φ) be of the form (1.1).…”