Toeplitz determinants associated with Ma-Minda classes of starlike and convex functions

TL;DR

This paper establishes sharp bounds for symmetric Toeplitz determinants derived from coefficients of Ma-Minda classes of starlike and convex functions, expanding known results and introducing new special cases.

Contribution

It provides new sharp bounds for Toeplitz determinants associated with specific subclasses of starlike functions, including several new special cases.

Findings

Sharp bounds for Toeplitz determinants are derived.

Results include new special cases and generalizations of known results.

The bounds relate to functions with specific geometric properties in the right half-plane.

Abstract

A starlike function $f$ is characterized by the quantity $zf'(z)/f(z)$ lying in the right half-plane. This paper deals with sharp bounds for certain symmetric Toeplitz determinants whose entries are the coefficients of the functions $f$ for which the quantity $zf'(z)/f(z)$ takes values in certain specific subset in the right half-plane. The results obtained include several new special cases and some known results.