Radius of Starlikeness for Bloch Functions

TL;DR

This paper investigates the radii within which Bloch functions, a class of normalized analytic functions with a specific derivative bound, are guaranteed to be starlike in the unit disc.

Contribution

It determines the radii of starlikeness for Bloch functions, expanding understanding of their geometric properties.

Findings

Established various starlikeness radii for Bloch functions

Provided bounds based on the derivative condition

Enhanced geometric function theory knowledge

Abstract

For normalised analytic functions $f$ defined on the open unit disc $\mathbb{D}$ satisfying the condition $\sup_{z\in \mathbb{D}}(1-|z^2|) |f'(z)|\leq 1$, known as Bloch functions, we determine various starlikeness radii.