Coefficient Functional and Bohr-Rogosinski Phenomenon for Analytic functions involving Semigroup Generators

TL;DR

This paper investigates coefficient bounds and growth estimates for semigroup generators, establishing sharp bounds and demonstrating Bohr-Rogosinski phenomena in geometric function theory.

Contribution

It introduces new sharp bounds for coefficient functionals and proves Bohr-Rogosinski phenomena specifically for semigroup generators.

Findings

Sharp bounds for second order Hankel determinant

Bounds for third order Toeplitz and Hermitian-Toeplitz determinants

Proof of Bohr-Rogosinski phenomenon for semigroup generators

Abstract

This paper examines the coefficient problems for the class of semigroup generators, a topic in complex dynamics that has recently been studied in context of geometric function theory. Further, sharp bounds of coefficient functional such as second order Hankel determinant, third order Toeplitz and Hermitian-Toeplitz determinants are derived. Additionally, the sharp growth estimates and the bounds of difference of successive coefficients are determined, which are used to prove the Bohr and the Bohr-Rogosinski phenomenon for the class of semigroup generators.