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2021•TURKISH JOURNAL OF MATHEMATICSOpen access

Hermitian-Toeplitz determinants for functions with bounded turning

KUMAR, VIRENDRA, CHO, NAK EUN

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Abstract

There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory. It is also, therefore, natural to explore the concept of the Hermitian-Toeplitz determinants for such functions. In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order $\alpha$, are obtained. \keywords{Analytic functions, functions with bounded turning of order $\alpha$, Hermitian-Toeplitz determinant

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What this paper is about

There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory. It is also, therefore, natural to explore the concept of the Hermitian-Toeplitz determinants for such functions. In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order $\alpha$, are obtained. \keywords{Analytic functions, functions with bounded turning of order $\alpha$, Hermitian-Toeplitz determinant

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Available abstract

There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory. It is also, therefore, natural to explore the concept of the Hermitian-Toeplitz determinants for such functions. In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order $\alpha$, are obtained. \keywords{Analytic functions, functions with bounded turning of order $\alpha$, Hermitian-Toeplitz determinant

Key concepts: Toeplitz matrix, Hermitian matrix, Bounded function, Mathematics, Levinson recursion, Pure mathematics, Order (exchange), Analytic function

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