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Symmetry
Volume 13
Issue 7
10.3390/sym13071274
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Article

The Third-Order Hermitian Toeplitz Determinant for Alpha-Convex Functions

by
Anna Dobosz
Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Ul. Słoneczna 54, 10-710 Olsztyn, Poland
Symmetry 2021, 13(7), 1274; https://doi.org/10.3390/sym13071274
Submission received: 24 June 2021 / Revised: 14 July 2021 / Accepted: 15 July 2021 / Published: 16 July 2021
(This article belongs to the Special Issue Special Functions and Polynomials)
Versions Notes

Abstract

Sharp lower and upper bounds of the second- and third-order Hermitian Toeplitz determinants for the class of α-convex functions were found. The symmetry properties of the arithmetic mean underlying the definition of α-convexity and the symmetry properties of Hermitian matrices were used.
Keywords: Hermitian Toeplitz determinants; univalent; convex; starlike; alpha-convex function; Carathéodory class Hermitian Toeplitz determinants; univalent; convex; starlike; alpha-convex function; Carathéodory class

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MDPI and ACS Style

Dobosz, A. The Third-Order Hermitian Toeplitz Determinant for Alpha-Convex Functions. Symmetry 2021, 13, 1274. https://doi.org/10.3390/sym13071274

AMA Style

Dobosz A. The Third-Order Hermitian Toeplitz Determinant for Alpha-Convex Functions. Symmetry. 2021; 13(7):1274. https://doi.org/10.3390/sym13071274

Chicago/Turabian Style

Dobosz, Anna. 2021. "The Third-Order Hermitian Toeplitz Determinant for Alpha-Convex Functions" Symmetry 13, no. 7: 1274. https://doi.org/10.3390/sym13071274

APA Style

Dobosz, A. (2021). The Third-Order Hermitian Toeplitz Determinant for Alpha-Convex Functions. Symmetry, 13(7), 1274. https://doi.org/10.3390/sym13071274

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