Radii of Starlikeness Associated with the Lemniscate of Bernoulli and the Left-Half Plane

TL;DR

This paper investigates the radii of starlikeness for specific classes of normalized analytic functions related to the lemniscate of Bernoulli and the left-half plane, expanding understanding of geometric function theory.

Contribution

It determines the SL-radii for various well-known function classes and explores radius problems linked to the left-half plane.

Findings

SL-radii for certain classes are explicitly calculated.

Radius problems for the left-half plane are addressed.

Results extend geometric function theory related to lemniscates.

Abstract

A normalized analytic function f defined on the open unit disk in the complex plane is in the class SL if zf'(z)/f(z) lies in the region bounded by the right-half of the lemniscate of Bernoulli given by |w^2 - 1| < 1. In the present investigation, the SL-radii for certain well-known classes of functions are obtained. Radius problems associated with the left-half plane are also investigated for these classes