Toeplitz determinants of Logarithmic coefficients for Starlike and Convex functions

TL;DR

This paper investigates sharp bounds for Toeplitz determinants formed from logarithmic coefficients of univalent functions, focusing on starlike and convex classes and their subclasses.

Contribution

It provides new sharp bounds for Toeplitz determinants associated with logarithmic coefficients of specific classes of univalent functions.

Findings

Established bounds for Toeplitz determinants of starlike functions.

Extended results to convex functions and subclasses.

Provided sharp bounds that improve existing estimates.

Abstract

In this study, we deal with the sharp bounds of certain Toeplitz determinants whose entries are the logarithmic coefficients of analytic univalent functions $f$ such that the quantity $z f'(z)/f(z)$ takes values in a specific domain lying in the right half plane. The established results provide the bounds for the classes of starlike and convex functions, as well as various of their subclasses.