Sharp Estimates of Hermitian Toeplitz Determinants for Some Subclasses of Sakaguchi Type Function Related to Sine Function

Abstract

Hermitian Toeplitz determinants are utilized across various fields, such as functional analysis, applied mathematics, physics, and technical sciences. This paper establishes a link with specific subclasses of analytic functions. Extensive research exists regarding estimating second and third Hankel determinants for normalized analytic functions within this domain. The current research seeks to establish precise upper and lower bounds for the second and third-order Hermitian Toeplitz determinants associated with specific novel subclasses of Sakaguchi-type functions, Ss∗(sin z), Sc∗(sin z) and Spq(sin z) related to the sine function. Further, the sharp estimates of Zalcman functional |an+m−1 − anam| for n = 2 and n = 2, m = 3 are considered.