Starlikeness associated with lemniscate of Bernoulli

TL;DR

This paper establishes sufficient conditions for analytic functions on the unit disk to be associated with the lemniscate of Bernoulli, using differential subordination techniques to analyze their starlikeness properties.

Contribution

It introduces new sufficient conditions for functions to be related to the lemniscate of Bernoulli via differential subordination methods.

Findings

Derived admissibility conditions for lemniscate of Bernoulli

Established criteria for starlikeness related to lemniscate

Applied differential subordination techniques to analytic functions

Abstract

For an analytic function $f$ on the unit disk $\mathbb{D}=\{z:|z|<1\}$ satisfying $f(0)=0=f'(0)-1,$ we obtain sufficient conditions so that $f$ satisfies $|(zf'(z)/f(z))^2-1|<1.$ The technique of differential subordination of first or second order is used. The admissibility conditions for lemniscate of Bernoulli are derived and employed in order to prove the main results.