Sharp bounds on Coefficient functionals of certain Sakaguchi functions

TL;DR

This paper establishes precise bounds on Hankel and Hermitian-Toeplitz determinants for specific subclasses of Sakaguchi functions, enhancing understanding of their coefficient behaviors and invariance properties.

Contribution

It provides the first sharp bounds on these determinants for Sakaguchi functions related to the lemniscate of Bernoulli and exponential functions.

Findings

Sharp bounds on Hankel determinants involving coefficients.

Sharp bounds on second Hermitian-Toeplitz determinants.

Discussion of invariance properties of the estimates.

Abstract

We determine sharp bounds on some Hankel determinants involving initial coefficients, inverse coefficients, and logarithmic inverse coefficients for two subclasses of Sakaguchi functions which are associated with the right half of the lemniscate of Bernoulli and the exponential function. Further, we compute sharp bounds on the second Hermitian-Toeplitz determinants involving logarithmic coefficients and logarithmic inverse coefficients. We also discuss invariant property for the obtained estimates with respect to various coefficients.