Hermitian-Toeplitz determinants for certain univalent functions

TL;DR

This paper derives sharp bounds for second and third order Hermitian-Toeplitz determinants within specific subclasses of univalent functions, enhancing understanding of their geometric properties.

Contribution

It introduces new bounds for Hermitian-Toeplitz determinants for generalized starlike and convex functions, expanding the analytical tools available for these classes.

Findings

Established sharp bounds for second and third order determinants.

Applied results to well-known subclasses of univalent functions.

Enhanced understanding of geometric function properties.

Abstract

Sharp upper and lower bounds for the second and third order Hermitian-Toepilitz determinants are obtained for some generalized subclasses of starlike and convex functions. Applications of these results are also discussed for several widely known classes.