"Upper bounds of Toeplitz determinants for a subclass of alpha-close-to-convex functions"

Abstract

"Let A be the class of P analytic functions in the unit disc U which are of the form $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$. For 0 ≤ α < 1, let C_α, be the class of all functions f ∈ A satisfying the condition ${Re}{f'(z)+αzf''(z)}>0$. We consider the Toeplitz matrices whose elements are the coefficients an of the function f in the class C_α. In this paper we obtain upper bounds for the Toeplitz determinants. "

Symmetric Toeplitz Determinants for Classes Defined by Post Quantum Operators Subordinated to the Limaçon Function

“…then the analytic characterization of the limaçon domain L s (D) is given by the inclusion relation (see [13] inclusions (9) and (10))…”

“…A Toeplitz determinant can be thought of as an "upside-down" Hankel determinant, in that Hankel determinant have constant entries along the reverse diagonal, whereas Toeplitz matrices have constant entries along the diagonal. In recent past, many researchers have focussed on finding sharp estimates for second and third order Toeplitz determinants [10], [7], etc.…”