Radius Constants of Sigmoid Starlike Functions

TL;DR

This paper investigates the radius constants of sigmoid starlike functions, providing sharp estimates for various subclasses and validating results graphically.

Contribution

It introduces new sharp radius bounds for sigmoid starlike functions and their subclasses, expanding understanding of their geometric properties.

Findings

Sharp radius constants established for sigmoid starlike functions

Graphical validation confirms the sharpness of the bounds

Results apply to several known subclasses of starlike functions

Abstract

In the present investigation, we study the class of Sigmoid starlike functions, given by $\mathcal{S}^*_{SG}=\{f\in\mathcal{A}: {zf'(z)}/{f(z)}\prec 2/(1+e^{-z})\}$ in context of estimating the sharp radius constants associated with several known subclasses of starlike functions. Further, graphical validation for the sharpness of results is also provided.